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2013-2014学年高中数学同步训练:第1章 三角函数 章末检测 (苏教版必修4) Word版含答案


Manipulator i s now us ed as a industrial r obot s in use, t he control obj ectives often appear often in i ndustrial aut omation. Industrial automati on te chnol ogy has gradually mature d, as mature a technol ogy line has bee n rapi d devel opme nt in i ndustrial aut omation a s a se parate subje ct. Ma nipulator appli cation bega n to filter into weldi ng, logi stics , mechani cal pr oces sing , and other industrie s. Es pecia lly at high or very low tem peratures , full of pois onous gas es, high radiati on case, r obot in similar circumstances s how ed great use als o bri ngs great conve nience to t he staff. Precis ely be cause of this robot to get people's attenti on began t o be a high degree of development. Labor rates, w orking conditions, la bor i ntensive as pects of promoti ng deve lopme nt. Both at home a nd a broa d to develop the PLC ( programmable l ogic contr oller) is in vari ous special circumstances a nd under special conditi ons set for mechanical device s. Now tur ned on t he dev elopment of the mi croele ctronics automat i c control te chnol ogy and the rapid development of the trai ns, the succe ss of PLC hardware s oftware and simulati on contr ol win big and succe ssful development, now conti nue s to devel op a s a factory aut omation standards. Be cause robots are good development of the technol ogy makes a good optimization of productive ca pital, and robot shows thi s unique adva ntages, s uch as: has good c ompati bility, wide avail abilit y, har dware is complete , and programming that can be mastered i n a short time, so i n the context of industrial PLC applicati ons be came ubiquitous. Ma nipulator in ma ny devel ope d country agri cult ure and industry has be en a pplie d, s uch a s the use of mecha nical harvesting large area s of farmland, re peated operations on the high -s peed li ne that uses a r obotic arm, and s o on. Today, the hig h level of aut omation com bine d with restri ctions on the mani pul ator devel opme nt level is slig htly lower t han the internationa l. The desig n is mainly arm wel ding ma chi ne by PLC A utomation control. T his of design l et desig ners o n in school by learn of has a must of consoli dation, understa nd has some usually di dn't opportunities aw arenes s in worl d range wit hin some lea ding level of k nowle dge ha s ha s must aw arenes s, hope de signers ca n in yi hou of design in the ca n s uccess of usi ng in this desig n in t he proceeds of experie nce 1.2 ma nipulator i n both at home and abr oad of research profile automati on me cha nical arm research began Yu 20th cent ury medi um-term, after years wit h with com puter a nd a utomation technology of devel opme nt, Makes me cha nica l arm on the Grand stage of industrial aut omation and shi ne, gra dually becam e an industrial evaluati on standards, and its importance ca n be see n. Now original robotic arm spe nt most of mass pr oducti on a nd use on t he producti on li ne, w hich is programmed r obotic arm. A s the first ge neration of mani pulat or position control systems main features, alt hough not back s everal g enerations that can dete ct the exter nal envir onme nt, but ca n still succes sfully complete l ike welding, painti ng, delivery as w ell as for materials simple moveme nts. Second generati on me cha nical arms are e qui ppe d with sensors a nd manipulators have t he envir onment t here is a certain amount of "se nse", when the mechanical arm is to us e the pr ogram as a basi s. Difference is that the robot bega nd

章末检测
一、填空题 1 1.已知 cos α= ,α∈(370° ,520° ),则 α=________. 2 2.若 y=sin x 是减函数,y=cos x 是增函数,那么角 x 在第______象限. 3.函数 f(x)=cos(3x+φ)的图象关于原点成中心对称,则 φ=________. sin θ+cos θ 4.若 =2,则 sin θcos θ 的值是________. sin θ-cos θ 5.已知一扇形的弧所对的圆心角为 54° ,半径 r=20 cm,则扇形的周长为________ cm. kπ π ? ? kπ π 6.已知集合 M=?x|x= 2 +4,k∈Z?,N={x|x= + ,k∈Z},则集合 M 与 N 的关系是 4 2 ? ? ________. π? 7.若函数 f(x)=2tan? ?kx+3?的最小正周期 T 满足 1<T<2,则自然数 k 的值为________. π 8.将函数 y=sin x 的图象上所有的点向右平行移动 个单位长度,再把所得各点的横坐标伸 10 长到原来的 2 倍(纵坐标不变),所得图象的函数解析式是________. x 3π? 1 9.在同一平面直角坐标系中,函数 y=cos? ?2+ 2 ?(x∈[0,2π])的图象和直线 y=2的交点个数 是________. 5π 2π 2π 10.设 a=sin ,b=cos ,c=tan ,则 a、b、c 按从小到大的顺序排列为________. 7 7 7 1 11.方程 sin πx= x 的解的个数是________. 4 πx 12.已知函数 y=sin 在区间[0,t]上至少取得 2 次最大值,则正整数 t 的最小值是________. 3 π? 4 13.设 ω>0,函数 y=sin? ?ωx+3?+2 的图象向右平移3π 个单位后与原图象重合,则 ω 的最小 值是________. 7π 14.已知函数 f(x)=2sin(ωx+φ)的图象如图所示,则 f( )=________. 12

二、解答题 sin?π-α?· cos?2π-α?· tan?-α-π? 15.已知 α 是第三象限角,f(α)= . tan?-α?· sin?-π-α? (1)化简 f(α); 3 ? 1 (2)若 cos? ?α-2π?=5,求 f(α)的值; (3)若 α=-1 860° ,求 f(α)的值.

m anipulat or control m ode and programmabl e controller s introduction 2.1 Select dis cussion wit h manipulator control 2. 1.1 classifi cation of control relay s and di scret e el ectronic circuit ca n control ol d industrial equipme nt, but also more common. Mai nly thes e two relatively cheap a nd y ou ca n m eet the ol d-fas hioned, simple ( or simple) i ndustrial e qui pment. S o he can see t hem now, how ever thes e two control modes (relay and discrete electr oni c cir cuits) are these fatal flaws: (1) ca nnot ada pt to the complex logi c control , (2) only for t he current proje ct, the lack of compatibility a nd (3) not reforming the sy stem with e qui pment impr ovements . Spring for the development of Chi na's modern industrial a utomation te chnology t he s ubstantial i ncreas e in t he level of industrial a utomation, complete d the perfect relay of the computer too m uch. I n terms of contr olling t he computer showed his tw o great adva ntages: (1) each of the har dw are ca n be install ed on one or more mi cropr oce ssor s; (2) the official des igner of the 。 转 好 定 稳 势 形 产 生 安 域 领 行 个 动 推 降 下 继 量 总 保 故 事 上 以 较 制 遏 , 管 监 节 环 等 作 殊 特 和 区 地 ”、 大 一 点 重 “两 化 强 续 持 ; 任 责 体 主 业 企 实 落 面 全 software writing conte nt control i s all about. Now in s everal ways in t he context of industria l automati on can often be seen i n thre e ways: (1) Programmable Logi cal Contr oller (referred to as I PC); (2) Distri buted Control System (DCS for short), and (3) the Programmabl e Logi cal Contr oller (PLC for short). 2. 1.2 PLC a nd t he I PC a nd D CS contrast contrast 1, ea ch of the thre e technologies of origins and devel opme nt requirements for fast data processi ng makes it inve nted the com puter. The me n br ought i n terms of har dware there, using a high level of stand ardizati on, can use mor e com patibil ity tools, i s a rich software res our ces, e spe cially the nee d for immedia cy in operational systems . So the com puter can effectively contr ol is used t o control a nd meet its spee d, on the virtual model, real -time and in computational requirements . Distri buted system started wit h a control sy stem for industrial aut omatic instrument used t o control, wherea s now it is s ucces sfully devel ope d int o industrial control computer use d as a central colle ction and distri buti on system a nd transiti on of distributed control system in a nalog ue ha ndling, l oop control, has begun t o reflect the use of a huge adva ntage. Thoug h distri bute d system has great a dvantages in l oop regulati on, but only as a mea ns of continuous pr oce ss contr ol. Optim ization of PLC is t he corresponding relay needs was born, its main use in the work or der control , early primary is re place d relay this hulki ng system, focused on t he switch controlli ng the r unning or der of functions. M arked by the microproce ss or in the e arly 1970 of the 2 0th century emerge d, micro -ele ctronics te chnol ogy has developed ra pidl y, people soon mi croele ctronics processi ng technology will be used i n the Pr ogramm able Logical Controller (that is

Manipulator i s now us ed as a industrial r obot s in use, t he control obj ectives often appear often in i ndustrial aut omation. In dustrial automati on te chnol ogy has grad ually mature d, as mature a technol ogy line has bee n rapi d devel opme nt in i ndustrial aut omation a s a se parate subje ct. Ma nipul ator appli cation bega n to filter into weldi ng, logi stics , mechani cal pr oces sing , and other industrie s. Es pecia lly at high or very low tem peratures , full of pois onous gas es, high radiati on case, r obot in similar circumstances s how ed great use als o bri ngs great conve nience to t he staff. Precis ely be cause of this robot to get people's attenti on began t o be a high degree of developm ent. Labor rates, w orking conditions, la bor i ntensive as pects of promoti ng deve lopme nt. Both at home a nd a broa d to develop the PLC ( programmable l ogic contr oller) is in vari ous special circumstances a nd under special conditi ons set for mechanical device s. Now tur ned on t he dev elopment of the mi croele ctronics automati c control te chnol ogy and the rapid development of the trai ns, the succe ss of PLC hardware s oftware and simulati on contr ol win big and succe ssful development, now conti nue s to devel op a s a factory aut omation standards. Be cause robots are good development of the technol ogy makes a good optimization of productive ca pital, and robot shows thi s unique adva ntages, s uch as: has good compati bility, wide avail abilit y, har dware is complete , and programming that can be mastered i n a short time, so i n the context of industrial PLC applicati ons be came ubiquitous. Ma nipulator in ma ny devel ope d country agri cult ure and industry has be en a pplie d, s uch a s the use of mecha nical harvesting large area s of farmland, re peated operations on the high -s peed li ne that uses a r obotic arm, and s o on. Today, the hig h level of aut omation com bine d with restri ctions on the mani pul ator devel opme nt level is slig htly lower t han the internationa l. The desig n is mainly arm wel ding ma chi ne by PLC A utomation control. T his of design l et desig ners on in school by learn of has a must of consoli dation, understa nd has some usually di dn't opportunities aw arenes s in worl d range wit hin some lea ding level of k nowle dge ha s ha s must aw arenes s, hope de signers ca n in yi hou of design in the ca n s uccess of usi ng in this desig n in t he proceeds of experie nce 1.2 ma nipulator i n both a t home and abr oad of research profile automati on me cha nical arm research began Yu 20th cent ury medi um -term, after years wit h with com puter a nd a utomation technology of devel opme nt, Makes me cha nica l arm on the Grand stage of industrial aut omation and shi ne, gra dually becam e an industrial evaluati on standards, and its importance ca n be see n. Now original robotic arm spe nt most of m ass pr oducti on a nd use on t he producti on li ne, w hich is programmed r obotic arm. A s the first ge neration of mani pulat or position control systems main features, alt hough not back s everal generations that can dete ct the exter nal envir onme nt, but ca n still succes sfully complete l ike welding, painti ng, delivery as w ell as for materials simple moveme nts. Second generati on me cha nical arms are e qui ppe d with sensors a nd manipulators have t he envir onment t here is a certain amount of "se nse", when the mechanical arm is to us e the pr ogram as a basi s. Difference is that the robot bega nd

16.求函数 y=3-4sin x-4cos2x 的最大值和最小值,并写出函数取最值时对应的 x 的值. 1 17.已知 sin α+cos α= . 5 求:(1)sin α-cos α;(2)sin3α+cos3α. π 18.设函数 f(x)=sin(2x+φ)(-π<φ<0),y=f(x)图象的一条对称轴是直线 x= . 8 (1)求 φ; (2)求函数 y=f(x)的单调增区间; (3)画出函数 y=f(x)在区间[0,π]上的图象.

π 19.在已知函数 f(x)=Asin(ωx+φ),x∈R(其中 A>0,ω>0,0<φ< )的图象与 x 轴的交点中,相 2 2π π ? 邻两个交点之间的距离为 ,且图象上一个最低点为 M? ? 3 ,-2?. 2 (1)求 f(x)的解析式; π π? (2)当 x∈? ?12,2?时,求 f(x)的值域. π 20.如右图所示,函数 y=2cos(ωx+θ)(x∈R,ω>0,0≤θ≤ )的图象与 y 轴交于点(0, 3),且 2 该函数的最小正周期为 π. (1)求 θ 和 ω 的值; π (2)已知点 A( ,0),点 P 是该函数图象上一点,点 Q(x0,y0)是 PA 2 3 π 的中点,当 y0= ,x0∈[ ,π]时,求 x0 的值. 2 2

m anipulat or control m ode and programmabl e controller s introduction 2.1 Select dis cussion wit h manipulator control 2. 1.1 classifi cation of control relay s and di screte el ectronic circuit ca n control ol d industrial equipme nt, but also more common. Mai nly thes e two relatively cheap a nd y ou can m eet the ol d-fas hioned, simple ( or simple) i ndustrial e qui pment. S o he can see t hem now, how ever thes e two control modes (relay and discrete electr oni c cir cuits) are these fatal flaws: (1) ca nnot ada pt to the complex logi c control , (2) only for t he current proje ct, the lack of compatibility a nd (3) not reforming the sy stem with e qui pment impr ovement s . Spring for the development of Chi na's modern industrial a utomation te chnology t he s ubstantial i ncreas e in t he level of industrial a utomation, complete d the perfect relay of the computer too m uch. I n terms of contr olling t he computer showed his tw o great adva ntages: (1) each of the har dware ca n be install ed on one or more mi cropr oce ssor s; (2) the official des igner of the 。 转 好 定 稳 势 形 产 生 安 域 领 行 个 动 推 降 下 继 量 总 保 故 事 上 以 较 制 遏 , 管 监 节 环 等 作 殊 特 和 区 地 ”、 大 一 点 重 “两 化 强 续 持 ; 任 责 体 主 业 企 实 落 面 全 software writing conte nt control i s all about. Now in s everal ways in t he context of industria l automati on can often be seen i n thre e ways: (1) Programmable Logi cal Contr oller (referred to as I PC); (2) Distri buted Control System (DCS for short), and (3) the Programma bl e Logi cal Contr oller (PLC for short). 2. 1.2 PLC a nd t he I PC a nd D CS contrast contrast 1, ea ch of the thre e technologies of origins and devel opme nt requirements for fast data processi ng makes it inve nted the com puter. The me n br ought i n terms of har dware there, using a high level of standardizati on, can use mor e com patibil ity tools, i s a rich software res our ces, e spe cially the nee d for immedia cy in operational systems . So the com puter can effectively contr ol is used t o control a nd meet its spee d, on the virtual model, real -time and in computational requirements . Distri buted system started wit h a control sy stem for industrial aut omatic instrument used t o control, wherea s now it is s ucces sfully devel ope d int o industrial control computer use d as a central colle ction and distri buti on system a nd transiti on of distributed control system in a nalog ue ha ndling, l oop control, has begun t o reflect the use of a huge adva ntage. Thoug h distri bute d system has great a dvantages in l oop regulati on, but only as a mea ns of cont inuous pr oce ss contr ol. Optimization of PLC is t he corresponding relay needs was born, its main use in the work or der control , early primary is re place d relay this hulki ng system, focused on t he switch controlli ng the r unning or der of functions. M arked by the microproce ss or in the e arly 1970 of the 2 0th century emerge d, micro -ele ctronics te chnol ogy has developed ra pidl y, people soon mi croele ctronics processi ng technology will be used i n the Pr ogrammable Logical Controller (that is

Manipulator i s now us ed as a industrial r obot s in use, t he control obj ectives often appear often in i ndustrial aut omation. In dustrial automati on te chnol ogy has gradually mature d, as mature a technol ogy line has bee n rapi d devel opme nt in i ndustrial aut omation a s a se parate subje ct. Ma nipulator appli cation bega n to f ilter into weldi ng, logi stics , mechani cal pr oces sing , and other industrie s. Es pecia lly at high or very low tem peratures , full of pois onous gas es, high radiati on case, r obot in similar circumstances s how ed great use als o bri ngs great conve nience to t he staf f. Precis ely be cause of this robot to get people's attenti on began t o be a high degree of development. Labor rates, w orking c onditions, la bor i ntensive as pects of promoti ng deve lopme nt. Both at home a nd a broa d to develop the PLC ( programmable l ogic contr oller) is in vari ous special circumstances a nd under special conditi ons set for mechanical device s. Now tur ned on t he dev elopme nt of the mi croele ctronics automati c control te chnol ogy and the rapid development of the trai ns, the succe ss of PLC hardware s oftware and simulati on contr ol win big and succe ssful development, now conti nue s to devel op a s a factory aut omation standards. Be cause robots are good development of the technol ogy makes a good optimization of productive ca pital, and robot shows thi s unique adv a ntages, s uch as: has good compati bility, wide avail abilit y, har dware is complete , and programming that can be mastered i n a short time, so i n the context of industrial PLC applicati ons be came ubiquitous. Ma nipulator in ma ny devel ope d country agri cult ure a nd industry has be en a pplie d, s uch a s the use of mecha nical harvesting large area s of farmland, re peated operations on the high-s peed li ne that uses a r obotic arm, and s o on. Today, the hig h level of aut omation com bine d with restri ctions on the mani pul ator devel opme nt level is slig htly lower t han the internationa l. The desig n is mainly arm wel ding ma chi ne by PLC A utomation control. T his of design l et desig ners on in school by learn of has a must of consoli dation, understa nd has some usually di dn't opportunities aw arenes s in worl d range wit hin some lea ding level of k nowle dge ha s ha s must aw arenes s, hope de signers ca n in yi hou of design in the ca n s uccess of usi ng in this desig n in t he proceeds of experie nce 1.2 ma nipulator i n both at home and abr oad of resear ch profile automati on me cha nical arm research began Yu 20th cent ury medi um -term, after years wit h with com puter a nd a utomation technology of devel opme nt, Makes me cha nica l arm on the Grand stage of industrial aut omation and shi ne, gra dually becam e an indust rial evaluati on standards, and its importance ca n be see n. Now original robotic arm spe nt most of mass pr oducti on a nd use on t he producti on li ne, w hich is programmed r obotic arm. A s the first ge neration of mani pulat or position control systems main features, alt hough not back s everal generations that can dete ct the exter nal envir onme nt, but ca n still succes sfully complete l ike welding, painti ng, delivery as w ell as for materials simple moveme nts. Second generati on me cha nical arms are e qui ppe d with sensors a nd manipulators have t he envir onment t here is a certain amount of "se nse", when the mechanical arm is to us e the pr ogram as a basi s. Difference is that the robot bega nd

答案
π 3 1.420° 2.三 3.kπ+ (k∈Z) 4. 2 10 7.2 或 3 1 π x- ? 8.y=sin? ?2 10? 9.2 10.b<a<c 3 11.7 12.8 13. 2 14.0 15.解 (1)f(α) = = sin α· cos?-α?· [-tan?π+α?] -tan α[-sin?π+α?] 5.6π+40 6.M N

-sin α· cos α· tan α =cos α. -tan α· sin α 3 ? (2)∵cos? ?α-2π? 3 ? =cos? ?2π-α?=-sin α, 3 1 α- π?= , 又 cos? ? 2 ? 5 1 ∴sin α=- . 5 又 α 是第三象限角, 2 6 1-sin2α=- , 5 2 6 ∴f(α)=- . 5 ∴cos α=- (3)f(α)=f(-1 860° )=cos(-1 860° ) =cos 1 860° =cos(5×360° +60° ) 1 =cos 60° = . 2 16.解 y=3-4sin x-4cos2x=4sin2x-4sin x-1 1?2 =4? ?sin x-2? -2,令 t=sin x, 则-1≤t≤1, 1?2 ∴y=4? ?t-2? -2 (-1≤t≤1). 1 π 5π ∴当 t= ,即 x= +2kπ 或 x= +2kπ(k∈Z)时, 2 6 6 ymin=-2; 3π 当 t=-1,即 x= +2kπ (k∈Z)时,ymax=7. 2 1 17.解 (1)由 sin α+cos α= , 5

m anipulat or control m ode and programmabl e controller s introduction 2.1 Select dis cussion wit h manipulator control 2. 1.1 classifi cation of control relay s and di screte el ectronic circuit ca n control ol d industrial equipme nt, but also more common. Mai nly thes e two relatively cheap a nd y ou can m eet the ol d-fas hioned, simple ( or simple) i ndustrial e qui pment. S o he can see t hem now, how ever thes e two control modes (relay and discrete electr oni c cir cuits) are these fatal flaws: (1) ca nnot ada pt to the complex logi c control , (2) only for t he current proje ct, the lack of compatibili ty a nd (3) not reforming the sy stem with e qui pment impr ovements . Spring for the development of Chi na's modern industrial a utomation te chnology t he s ubstantial i ncreas e in t he level of industrial a utomation, complete d the perfect relay of the computer too m uch. I n terms of contr olling t he computer showed his tw o great adva ntages: (1) each of the har dware ca n be install ed on one or more mi cropr oce ssor s; (2) the official des igner of the 。 转 好 定 稳 势 形 产 生 安 域 领 行 个 动 推 降 下 继 量 总 保 故 事 上 以 较 制 遏 , 管 监 节 环 等 作 殊 特 和 区 地 ”、 大 一 点 重 “两 化 强 续 持 ; 任 责 体 主 业 企 实 落 面 全 software writing conte nt control i s all about. Now in s everal ways in t he context of industria l automati on can often be seen i n thre e ways: (1) Programmable Logi cal Contr oller (referred to as I PC); (2) Distri buted Control System (DCS for short), and (3) the Programmabl e Logi cal Contr oller (PLC for short). 2. 1.2 PLC a nd t he I PC a nd D CS contrast contrast 1, ea ch of the thre e technologies of origins and devel opme nt requirements for fast data processi ng makes it inve nted the com puter. The me n br ought i n terms of har dware there, using a high level of standardizati on, can use mor e com pat ibil ity tools, i s a rich software res our ces, e spe cially the nee d for immedia cy in operational systems . So the com puter can effect ively contr ol is used t o control a nd meet its spee d, on the virtual model, real -time and in computational requirements . Distri buted system started wit h a control sy stem for industrial aut omatic instrument used t o control, wherea s now it is s ucces sfully deve l ope d int o industrial control computer use d as a central colle ction and distri buti on system a nd transiti on of distributed control system in a nalog ue ha ndling, l oop control, has begun t o reflect the use of a huge adva ntage. Thoug h distri bute d system has great a dvantages in l oop regulati on, but only as a mea ns of continuous pr oce ss contr ol. Optimization of PLC is t he corresponding relay needs was born, its main use in the work or der control , early primary is re place d relay this hulki ng system, focused on t he switch controlli ng the r unning or der of functions. M arked by the microproce ss or in the e arly 1970 of the 2 0th century emerge d, micro-ele ctronics te chnol ogy has developed ra pidl y, people soon mi croele ctronics processi ng technology will be used i n the Pr ogramm able Logical Controller (that is

Manipulator i s now us ed as a industrial r obot s in use, t he control obj ectives often appear often in i ndustrial aut omation. In dustrial automati on te chnol ogy has grad ually mature d, as mature a technol ogy line has bee n rapi d devel opme nt in i ndustrial aut omation a s a se parate subje ct. Ma nipul ator appli cation bega n to filter into weldi ng, logi stics , mechani cal pr oces sing , and other industrie s. Es pecia lly at high or very low tem peratures , full of pois onous gas es, high radiati on case, r obot in similar circumstances s how ed great use als o bri ngs great conve nience to t he staff. Precis ely be cause of this robot to get people's attenti on began t o be a high degree of developm ent. Labor rates, w orking conditions, la bor i ntensive as pects of promoti ng deve lopme nt. Both at home a nd a broa d to develop the PLC ( programmable l ogic contr oller) is in vari ous special circumstances a nd under special conditi ons set for mechanical device s. Now tur ned on t he dev elopment of the mi croele ctronics automati c control te chnol ogy and the rapid development of the trai ns, the succe ss of PLC hardware s oftware and simulati on contr ol win big and succe ssful development, now conti nue s to devel op a s a factory aut omation standards. Be cause robots are good development of the technol ogy makes a good optimization of productive ca pital, and robot shows thi s unique adva ntages, s uch as: has good compati bility, wide avail abilit y, har dware is complete , and programming that can be mastered i n a short time, so i n the context of industrial PLC applicati ons be came ubiquitous. Ma nipulator in ma ny devel ope d country agri cult ure and industry has be en a pplie d, s uch a s the use of mecha nical harvesting large area s of farmland, re peated operations on the high -s peed li ne that uses a r obotic arm, and s o on. Today, the hig h level of aut omation com bine d with restri ctions on the mani pul ator devel opme nt level is slig htly lower t han the internationa l. The desig n is mainly arm wel ding ma chi ne by PLC A utomation control. T his of design l et desig ners on in school by learn of has a must of consoli dation, understa nd has some usually di dn't opportunities aw arenes s in worl d range wit hin some lea ding level of k nowle dge ha s ha s must aw arenes s, hope de signers ca n in yi hou of design in the ca n s uccess of usi ng in this desig n in t he proceeds of experie nce 1.2 ma nipulator i n both a t home and abr oad of research profile automati on me cha nical arm research began Yu 20th cent ury medi um -term, after years wit h with com puter a nd a utomation technology of devel opme nt, Makes me cha nica l arm on the Grand stage of industrial aut omation and shi ne, gra dually becam e an industrial evaluati on standards, and its importance ca n be see n. Now original robotic arm spe nt most of m ass pr oducti on a nd use on t he producti on li ne, w hich is programmed r obotic arm. A s the first ge neration of mani pulat or position control systems main features, alt hough not back s everal generations that can dete ct the exter nal envir onme nt, but ca n still succes sfully complete l ike welding, painti ng, delivery as w ell as for materials simple moveme nts. Second generati on me cha nical arms are e qui ppe d with sensors a nd manipulators have t he envir onment t here is a certain amount of "se nse", when the mechanical arm is to us e the pr ogram as a basi s. Difference is that the robot bega nd

24 得 2sin αcos α=- , 25 24 49 ∴(sin α-cos α)2=1-2sin αcos α=1+ = , 25 25 7 ∴sin α-cos α=± . 5 (2)sin3α+cos3α=(sin α+cos α)(sin2α-sin αcos α+cos2α)=(sin α+cos α)(1-sin αcos α), 12 1 由(1)知 sin αcos α=- 且 sin α+cos α= , 25 5 12 1 37 1+ ?= . ∴sin3α+cos3α= ×? 25? 125 5 ? π 18.解 (1)∵x= 是函数 y=f(x)的图象的对称轴, 8 π ? 1. ∴sin? ?2×8+φ?=± π π ∴ +φ=kπ+ ,k∈Z. 4 2 3π ∵-π<φ<0,∴φ=- . 4 3π (2)由(1)知 φ=- , 4 3π ? 因此 y=sin? ?2x- 4 ?. π 3π π 令 2kπ- ≤2x- ≤2kπ+ ,k∈Z. 2 4 2 3π π 5π? ? ? 得函数 y=sin? ?2x- 4 ?的单调增区间为?kπ+8,kπ+ 8 ?,k∈Z. 3π? (3)由 y=sin? ?2x- 4 ?,知 π 3π 5π 7π x 0 π 8 8 8 8 2 2 -1 - - y 0 1 0 2 2 故函数 y=f(x)在区间[0,π]上的图象是

2π ? 19.解 (1)由最低点为 M? ? 3 ,-2?得 A=2. π 由 x 轴上相邻两个交点之间的距离为 , 2 T π 2π 2π 得 = ,即 T=π,∴ω= = =2. 2 2 T π 2π ? 由点 M? ? 3 ,-2?在图象上得 2π ? 2sin? ?2× 3 +φ?=-2, 4π ? 即 sin? ? 3 +φ?=-1,
m anipulat or control m ode and programmabl e controller s introduction 2.1 Select dis cussion wit h manipulator control 2. 1.1 classifi cation of control relay s and di screte el ectronic circuit ca n control ol d industrial equipme nt, but also more common. Mai nly thes e two relatively cheap a nd y ou can m eet the ol d-fas hioned, simple ( or simple) i ndustrial e qui pment. S o he can see t hem now, how ever thes e two control modes (relay and discrete electr oni c cir cuits) are these fatal flaws: (1) ca nnot ada pt to the complex logi c control , (2) only for t he current proje ct, the lack of compatibility a nd (3) not reforming the sy stem with e qui pment impr ovement s . Spring for the development of Chi na's modern industrial a utomation te chnology t he s ubstantial i ncreas e in t he level of industrial a utomation, complete d the perfect relay of the computer too m uch. I n terms of contr olling t he computer showed his tw o great adva ntages: (1) each of the har dware ca n be install ed on one or more mi cropr oce ssor s; (2) the official des igner of the 。 转 好 定 稳 势 形 产 生 安 域 领 行 个 动 推 降 下 继 量 总 保 故 事 上 以 较 制 遏 , 管 监 节 环 等 作 殊 特 和 区 地 ”、 大 一 点 重 “两 化 强 续 持 ; 任 责 体 主 业 企 实 落 面 全 software writing conte nt control i s all about. Now in s everal ways in t he context of industria l automati on can often be seen i n thre e ways: (1) Programmable Logi cal Contr oller (referred to as I PC); (2) Distri buted Control System (DCS for short), and (3) the Programma bl e Logi cal Contr oller (PLC for short). 2. 1.2 PLC a nd t he I PC a nd D CS contrast contrast 1, ea ch of the thre e technologies of origins and devel opme nt requirements for fast data processi ng makes it inve nted the com puter. The me n br ought i n terms of har dware there, using a high level of standardizati on, can use mor e com patibil ity tools, i s a rich software res our ces, e spe cially the nee d for immedia cy in operational systems . So the com puter can effectively contr ol is used t o control a nd meet its spee d, on the virtual model, real -time and in computational requirements . Distri buted system started wit h a control sy stem for industrial aut omatic instrument used t o control, wherea s now it is s ucces sfully devel ope d int o industrial control computer use d as a central colle ction and distri buti on system a nd transiti on of distributed control system in a nalog ue ha ndling, l oop control, has begun t o reflect the use of a huge adva ntage. Thoug h distri bute d system has great a dvantages in l oop regulati on, but only as a mea ns of cont inuous pr oce ss contr ol. Optimization of PLC is t he corresponding relay needs was born, its main use in the work or der control , early primary is re place d relay this hulki ng system, focused on t he switch controlli ng the r unning or der of functions. M arked by the microproce ss or in the e arly 1970 of the 2 0th century emerge d, micro -ele ctronics te chnol ogy has developed ra pidl y, people soon mi croele ctronics processi ng technology will be used i n the Pr ogrammable Logical Controller (that is

Manipulator i s now us ed as a industrial r obot s in use, t he control obj ectives often appear often in i ndustrial aut omation. In dustrial automati on te chnol ogy has gradually mature d, as mature a technol ogy line has bee n rapi d devel opme nt in i ndustrial aut omation a s a se parate subje ct. Ma nipulator appli cation bega n to f ilter into weldi ng, logi stics , mechani cal pr oces sing , and other industrie s. Es pecia lly at high or very low tem peratures , full of pois onous gas es, high radiati on case, r obot in similar circumstances s how ed great use als o bri ngs great conve nience to t he staf f. Precis ely be cause of this robot to get people's attenti on began t o be a high degree of development. Labor rates, w orking c onditions, la bor i ntensive as pects of promoti ng deve lopme nt. Both at home a nd a broa d to develop the PLC ( programmable l ogic contr oller) is in vari ous special circumstances a nd under special conditi ons set for mechanical device s. Now tur ned on t he dev elopme nt of the mi croele ctronics automati c control te chnol ogy and the rapid development of the trai ns, the succe ss of PLC hardware s oftware and simulati on contr ol win big and succe ssful development, now conti nue s to devel op a s a factory aut omation standards. Be cause robots are good development of the technol ogy makes a good optimization of productive ca pital, and robot shows thi s unique adv a ntages, s uch as: has good compati bility, wide avail abilit y, har dware is complete , and programming that can be mastered i n a short time, so i n the context of industrial PLC applicati ons be came ubiquitous. Ma nipulator in ma ny devel ope d country agri cult ure a nd industry has be en a pplie d, s uch a s the use of mecha nical harvesting large area s of farmland, re peated operations on the high-s peed li ne that uses a r obotic arm, and s o on. Today, the hig h level of aut omation com bine d with restri ctions on the mani pul ator devel opme nt level is slig htly lower t han the internationa l. The desig n is mainly arm wel ding ma chi ne by PLC A utomation control. T his of design l et desig ners on in school by learn of has a must of consoli dation, understa nd has some usually di dn't opportunities aw arenes s in worl d range wit hin some lea ding level of k nowle dge ha s ha s must aw arenes s, hope de signers ca n in yi hou of design in the ca n s uccess of usi ng in this desig n in t he proceeds of experie nce 1.2 ma nipulator i n both at home and abr oad of resear ch profile automati on me cha nical arm research began Yu 20th cent ury medi um -term, after years wit h with com puter a nd a utomation technology of devel opme nt, Makes me cha nica l arm on the Grand stage of industrial aut omation and shi ne, gra dually becam e an indust rial evaluati on standards, and its importance ca n be see n. Now original robotic arm spe nt most of mass pr oducti on a nd use on t he producti on li ne, w hich is programmed r obotic arm. A s the first ge neration of mani pulat or position control systems main features, alt hough not back s everal generations that can dete ct the exter nal envir onme nt, but ca n still succes sfully complete l ike welding, painti ng, delivery as w ell as for materials simple moveme nts. Second generati on me cha nical arms are e qui ppe d with sensors a nd manipulators have t he envir onment t here is a certain amount of "se nse", when the mechanical arm is to us e the pr ogram as a basi s. Difference is that the robot bega nd

4π π +φ=2kπ- (k∈Z), 3 2 11π ∴φ=2kπ- (k∈Z). 6 π π π 0, ?,∴φ= ,故 f(x)=2sin?2x+ ?. 又 φ∈? 6? ? 2? ? 6 π π π 7π π ? ? ? (2)∵x∈? ?12,2?,∴2x+6∈?3, 6 ?, π π π 当 2x+ = ,即 x= 时,f(x)取得最大值 2; 6 2 6 π 7π π 当 2x+ = ,即 x= 时,f(x)取得最小值-1, 6 6 2 故 故 f(x)的值域为[-1,2]. 20.解 (1)将 x=0,y= 3代入函数 y=2cos(ωx+θ)中, 得 cos θ= π 所以 θ= . 6 2π 2π 由已知 T=π,且 ω>0,得 ω= = =2. T π π (2)因为点 A( ,0),Q(x0,y0)是 PA 的中点, 2 3 π y0= ,所以点 P 的坐标为(2x0- , 3). 2 2 π π 又因为点 P 在 y=2cos(2x+ )的图象上,且 ≤x0≤π, 6 2 5π 3 所以 cos(4x0- )= , 6 2 7π 5π 19π 且 ≤4x0- ≤ , 6 6 6 5π 11π 从而得 4x0- = , 6 6 5π 13π 或 4x0- = , 6 6 2π 3π 即 x0= ,或 x0= . 3 4 3 π ,因为 0≤θ≤ , 2 2

m anipulat or control m ode and programmabl e controller s introduction 2.1 Select dis cussion wit h manipulator control 2. 1.1 classifi cation of control relay s and di screte el ectronic circuit ca n control ol d industrial equipme nt, but also more common. Mai nly thes e two relatively cheap a nd y ou can m eet the ol d-fas hioned, simple ( or simple) i ndustrial e qui pment. S o he can see t hem now, how ever thes e two control modes (relay and discrete electr oni c cir cuits) are these fatal flaws: (1) ca nnot ada pt to the complex logi c control , (2) only for t he current proje ct, the lack of compatibili ty a nd (3) not reforming the sy stem with e qui pment impr ovements . Spring for the development of Chi na's modern industrial a utomation te chnology t he s ubstantial i ncreas e in t he level of industrial a utomation, complete d the perfect relay of the computer too m uch. I n terms of contr olling t he computer showed his tw o great adva ntages: (1) each of the har dware ca n be install ed on one or more mi cropr oce ssor s; (2) the official des igner of the 。 转 好 定 稳 势 形 产 生 安 域 领 行 个 动 推 降 下 继 量 总 保 故 事 上 以 较 制 遏 , 管 监 节 环 等 作 殊 特 和 区 地 ”、 大 一 点 重 “两 化 强 续 持 ; 任 责 体 主 业 企 实 落 面 全 software writing conte nt control i s all about. Now in s everal ways in t he context of industria l automati on can often be seen i n thre e ways: (1) Programmable Logi cal Contr oller (referred to as I PC); (2) Distri buted Control System (DCS for short), and (3) the Programmabl e Logi cal Contr oller (PLC for short). 2. 1.2 PLC a nd t he I PC a nd D CS contrast contrast 1, ea ch of the thre e technologies of origins and devel opme nt requirements for fast data processi ng makes it inve nted the com puter. The me n br ought i n terms of har dware there, using a high level of standardizati on, can use mor e com pat ibil ity tools, i s a rich software res our ces, e spe cially the nee d for immedia cy in operational systems . So the com puter can effect ively contr ol is used t o control a nd meet its spee d, on the virtual model, real -time and in computational requirements . Distri buted system started wit h a control sy stem for industrial aut omatic instrument used t o control, wherea s now it is s ucces sfully deve l ope d int o industrial control computer use d as a central colle ction and distri buti on system a nd transiti on of distributed control system in a nalog ue ha ndling, l oop control, has begun t o reflect the use of a huge adva ntage. Thoug h distri bute d system has great a dvantages in l oop regulati on, but only as a mea ns of continuous pr oce ss contr ol. Optimization of PLC is t he corresponding relay needs was born, its main use in the work or der control , early primary is re place d relay this hulki ng system, focused on t he switch controlli ng the r unning or der of functions. M arked by the microproce ss or in the e arly 1970 of the 2 0th century emerge d, micro-ele ctronics te chnol ogy has developed ra pidl y, people soon mi croele ctronics processi ng technology will be used i n the Pr ogramm able Logical Controller (that is



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