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1、高中数学高考总复习角的概念的推广及任意角的三角函数习题及详解高中数学高考总复习角的概念的推广及任意角的三角函数习题及详解 一、选择题 1(2010?广州检测)若sin0，则是( ) A(第一象限角 B(第二象限角 C(第三象限角 D(第四象限角 答案 C 解析 ?sin0?为第一、三象限角 ?为第三象限角( 2(2010?安徽省168中学联考)已知集合A,(x，y)|y,sinx，集合B,(x，y)|y,tanx，则A?B,( ) A(0,0) B(，0)，(0,0) C(x，y)|x,k，y,0，k?Z D(? 答案 C 解析 函数y,sinx与y,tanx图象的交点坐标为(k0)k?Z.
2、22,3(2010?河北正定中学模拟)已知角终边上一点Psin，cos，则角的最小正值,33为( ) 511A. B. 6625C. D. 33答案 B 23解析 由条件知cos,sin,sin, 33221sin,cos,cos, 33211?角为第四象限角?,2,故选B. 6652,4(2010?山东师大附中模拟)cos,( ) ,313A(, B(, 22clearly, for maintenance management. 4. install (1) all sorts of switches, sockets and other equipment should be insta
3、lled firmly, position accurate, when installing rocker panel, switches, switch should be consistent, generally up to close down to off switch should cut off the line. Switches the elevation and location of the socket should conform to the drawings, the same interior height difference should not be g
4、reater than 5mm. (2) liquid level automatic control device used in a variety of angle brackets, there should be galvanized. (3) fixed lamp hanging boxes are plastic with rotary table round table. (4) light bulb capacity of 100W or less, available resin lamp, 100W and the tide sealed lamps, porcelain
5、 lamps. (5) the wiring inside the lamp shall not be less than 0.4mm2 wires. (6) the chandelier with a weight of more than 3kg, the embedded hook-bolts, install lighting in the brick or concrete structures, should use expansion bolts or plastic tube, ban the use of wooden wedges instead. (7) the ceil
6、ing mounted light fixtures, border of the shade should cover Panel joints and snapped the ceiling panel, determine the size lamp open position, strictly according to the drawings. (8) the lamps arranged orderly, symmetrical when installing the vertical and horizontal center lines should be on the sa
7、me line, deviation is less than 5mm. (9) the emergency lighting installation: according to the design and specifications to determine location of evacuation lighting, signs should 13C. D. 22答案 A 5252,解析 cos,cos,cos17， ,3331,cos,. 325(2010?河南新乡市模拟)已知角终边上一点P(,4a,3a)(a0)，则sin的值为( ) 33A. B(, 5544C. D(,
8、55答案 B 22解析 ?a0?r,，,4a，3a，,5a 3a3?sin,故选B. r56(2010?广东佛山顺德区质检)函数f(x),sinx在区间a，b上是增函数，且f(a),1，a，bf(b),1，则cos,( ) 22A(0 B. 2C(,1 D(1 答案 D a，b解析 由条件知a,，2k (k?Z)b,，2k?cos,cos2k,1. 2227(2010?青岛市质检)已知a为等差数列，若a，a，a,，则cos(a，a)的值为( ) n1592813A(, B(, 2213C. D. 22答案 A 解析 由条件知,a，a，a,3a?a, 15955321?cos(a，a),cos2
9、a,cos,cos,故选A. 2853321118(2010?衡水市高考模拟)设a,logtan70?，b,logsin25?，c,logcos25?，则它们的222大小关系为( ) A(acb B(bca C(abc D(bacos25?sin25?0logx为减函数?acb. 29(2010?北京西城区抽检)设0|sin B(cos2tan D(cot2cot 答案 B 3解析 当,0时A、C、D不成立(如,则2,sin2,sin4632131333,tan2,3tan,cot2,cot,3而,3cot. 10(如图所示的程序框图，运行后输出结果为( ) A(1 B(2680 C(2010
10、 D(1340 答案 C nn,解析 ?f(n),2sin，1,2cos，1.由S,S，f(n)及n,n，1知此程序框图是,323n计算数列a,2cos，1的前2010项的和( n3232010,即S,2cos，1，2cos，1，2cos，1，2cos，1 ,333323201023,2cos，cos，cos，cos，2010,2335cos，cos，cos，,3333333456cos，cos，cos，2010,2010. 333二、填空题 clearly, for maintenance management. 4. install (1) all sorts of switches, s
11、ockets and other equipment should be installed firm含详解答案 ly, position accurate, when installing rocker panel, switches, switch should be consistent, generally up to close down to off switch should cut off the line. Switches the elevation and location of the socket should conform to the drawings, the
12、 same interior height difference should not be greater than 5mm. (2) liquid level automatic control device used in a variety of angle brackets, there should be galvanized. (3) fixed lamp hanging boxes are plastic with rotary table round table. (4) light bulb capacity of 100W or less, available resin
13、 lamp, 100W and the tide sealed lamps, porcelain lamps. (5) the wiring inside the lamp shall not be less than 0.4mm2 wires. (6) the chandelier with a weight of more than 3kg, the embedded hook-bolts, install lighting in the brick or concrete structures, should use expansion bolts or plastic tube, ba
14、n the use of wooden wedges instead. (7) the ceiling mounted light fixtures, border of the shade should cover Panel joints and snapped the ceiling panel, determine the size lamp open position, strictly according to the drawings. (8) the lamps arranged orderly, symmetrical when installing the vertical
15、 and horizontal center lines should be on the same line, deviation is less than 5mm. (9) the emergency lighting installation: according to the design and specifications to determine location of evacuation lighting, signs should311(2010?南京调研)已知角的终边经过点P(x，,6)，且tan,，则x的值为5_( 答案 10 ,63解析 根据题意知tan,所以x,10
16、. x512(已知?ABC是锐角三角形，则点P(cosB,sinA，tanB,cotC)，在第_象限( 答案 二 解析 ?ABC为锐角三角形?0A 20B0CB，C 2222?A,B0B,C0 2222,?y,sinx与y,tanx在0上都是增函数 ,2,?sinAsin,BtanBtan,C ,22sinAcosBtanBcotC?P在第二象限( ?13(在(0,2)内使sinxcosx成立的x的取值范围是_( 5答案 (，) 44解析 由三角函数定义结合三角函数线知在(0,2)内使sinxcosx成立的x的取值5范围为()( 44点评 要熟知单位圆中的三角函数线在三角函数值的大小中的应用(
17、 14(文)(2010?上海嘉定区模拟)如图所示，角的终边与单位圆(圆心在原点，半径为13,的圆)交于第二象限的点Acos，则cos,sin,_. ,57答案 , 5clearly, for maintenance management. 4. install (1) all sorts of switches, sockets and other equipment should be installed firmly, position accurate, when installing rocker panel, switches, switch should be consistent
18、, generally up to close down to off switch should cut off the line. Switches the elevation and location of the socket should conform to the drawings, the same interior height difference should not be greater than 5mm. (2) liquid level automatic control device used in a variety of angle brackets, the
19、re should be galvanized. (3) fixed lamp hanging boxes are plastic with rotary table round table. (4) light bulb capacity of 100W or less, available resin lamp, 100W and the tide sealed lamps, porcelain lamps. (5) the wiring inside the lamp shall not be less than 0.4mm2 wires. (6) the chandelier with
20、 a weight of more than 3kg, the embedded hook-bolts, install lighting in the brick or concrete structures, should use expansion bolts or plastic tube, ban the use of wooden wedges instead. (7) the ceiling mounted light fixtures, border of the shade should cover Panel joints and snapped the ceiling p
21、anel, determine the size lamp open position, strictly according to the drawings. (8) the lamps arranged orderly, symmetrical when installing the vertical and horizontal center lines should be on the same line, deviation is less than 5mm. (9) the emergency lighting installation: according to the desi
22、gn and specifications to determine location of evacuation lighting, signs should 高考总复习 3解析 由条件知sin, 547?cos,?cos,sin,. 5522(理)(2010?北京延庆县模拟)直线y,2x，1和圆x，y,1交于A，B两点，以x轴的正方向为始边，OA为终边(O是坐标原点)的角为，OB为终边的角为，则sin(，),_. 4答案 , 54222解析 将y,2x，1代入x，y,1中得5x，4x,0?x,0或,?A(0,1)54334,B,故sin,1cos,0sin,cos, ,55554?sin(
23、，),sincos，cossin,. 5点评 也可以由A(0,1)知, 24,?sin(，),sin，,cos,. ,25三、解答题 3115(已知角终边经过点P(x，,2)(x?0)，且cos,x.求sin，的值( 6tan解析 ?P(x,2)(x?0) 2?点P到原点的距离r,x，2. 3x3又cos,x?cos,x. 266x，2?x?0?x,?10?r,23. clearly, for maintenance management. 4. install (1) all sorts of switches, sockets and other equipment should be i
24、nstalled firm含详解答案 ly, position accurate, when installing rocker panel, switches, switch should be consistent, generally up to close down to off switch should cut off the line. Switches the elevation and location of the socket should conform to the drawings, the same interior height difference shoul
25、d not be greater than 5mm. (2) liquid level automatic control device used in a variety of angle brackets, there should be galvanized. (3) fixed lamp hanging boxes are plastic with rotary table round table. (4) light bulb capacity of 100W or less, available resin lamp, 100W and the tide sealed lamps,
26、 porcelain lamps. (5) the wiring inside the lamp shall not be less than 0.4mm2 wires. (6) the chandelier with a weight of more than 3kg, the embedded hook-bolts, install lighting in the brick or concrete structures, should use expansion bolts or plastic tube, ban the use of wooden wedges instead. (7
27、) the ceiling mounted light fixtures, border of the shade should cover Panel joints and snapped the ceiling panel, determine the size lamp open position, strictly according to the drawings. (8) the lamps arranged orderly, symmetrical when installing the vertical and horizontal center lines should be
28、 on the same line, deviation is less than 5mm. (9) the emergency lighting installation: according to the design and specifications to determine location of evacuation lighting, signs should当x,10时P点坐标为(10,2) 61由三角函数的定义有sin,5 6tan65，616?sin，,5, tan6665,61当x,10时同理可求得sin，,. tan6216(文)已知sin、cos是方程x,(3,1)
29、x，m,0的两根( (1)求m的值; sincos(2)求，的值( 1,cot1,tan解析 (1)由韦达定理可得 sin，cos,3,1 ?, , ,sin?cos,m ?由?得1，2sin?cos,4,23. 32将?代入得m,3满足,(3,1),4m?0 23故所求m的值为,3. 2sincossincos，,， (2)先化简:cot1,tancossin1,1,1,sincos2222,sincossincos,，,cos，sin sin,coscos,sincos,sin,3,1. 2(理)已知关于x的方程2x,(3，1)x，m,0的两根为sin和cos，且?(0,2)， sinco
30、s(1)求，的值; 1,cot1,tan(2)求m的值; (3)求方程的两根及此时的值( 解析 (1)由韦达定理可知 3，1,sin，cos, ?2 ,m sin?cos, ?,222sincossincos而，,， 1,cot1,tansin,coscos,sinclearly, for maintenance management. 4. install (1) all sorts of switches, sockets and other equipment should be installed firmly, position accurate, when installing r
31、ocker panel, switches, switch should be consistent, generally up to close down to off switch should cut off the line. Switches the elevation and location of the socket should conform to the drawings, the same interior height difference should not be greater than 5mm. (2) liquid level automatic contr
32、ol device used in a variety of angle brackets, there should be galvanized. (3) fixed lamp hanging boxes are plastic with rotary table round table. (4) light bulb capacity of 100W or less, available resin lamp, 100W and the tide sealed lamps, porcelain lamps. (5) the wiring inside the lamp shall not
33、be less than 0.4mm2 wires. (6) the chandelier with a weight of more than 3kg, the embedded hook-bolts, install lighting in the brick or concrete structures, should use expansion bolts or plastic tube, ban the use of wooden wedges instead. (7) the ceiling mounted light fixtures, border of the shade s
34、hould cover Panel joints and snapped the ceiling panel, determine the size lamp open position, strictly according to the drawings. (8) the lamps arranged orderly, symmetrical when installing the vertical and horizontal center lines should be on the same line, deviation is less than 5mm. (9) the emer
35、gency lighting installation: according to the design and specifications to determine location of evacuation lighting, signs should 高考总复习 3，1,sin，cos, 22，3(2)由?两边平方得1，2sincos, 23将?代入得m, 23(3)当m,时原方程变为 233122x,(1，3)x，,0解得x,x, 1222213sin,sin,22?或 ,13 cos,cos,22又?(0,2)?,或. 6317(周长为20cm的扇形面积最大时，用该扇形卷成圆锥的
36、侧面，求此圆锥的体积( 解析 设扇形半径为r弧长为l则l，2r,20 l,20,2r ?11S,rl,(20,2r)?r,(10,r)?r 22?当r,5时S取最大值( 此时l,10设卷成圆锥的底半径为R则2R,10 5?R, 2,15522,?圆锥的高h,5, ,225,1125,11522,V,Rh,?,. 2,333clearly, for maintenance management. 4. install (1) all sorts of switches, sockets and other equipment should be installed firm含详解答案 ly, p
37、osition accurate, when installing rocker panel, switches, switch should be consistent, generally up to close down to off switch should cut off the line. Switches the elevation and location of the socket should conform to the drawings, the same interior height difference should not be greater than 5m
38、m. (2) liquid level automatic control device used in a variety of angle brackets, there should be galvanized. (3) fixed lamp hanging boxes are plastic with rotary table round table. (4) light bulb capacity of 100W or less, available resin lamp, 100W and the tide sealed lamps, porcelain lamps. (5) th
39、e wiring inside the lamp shall not be less than 0.4mm2 wires. (6) the chandelier with a weight of more than 3kg, the embedded hook-bolts, install lighting in the brick or concrete structures, should use expansion bolts or plastic tube, ban the use of wooden wedges instead. (7) the ceiling mounted li
40、ght fixtures, border of the shade should cover Panel joints and snapped the ceiling panel, determine the size lamp open position, strictly according to the drawings. (8) the lamps arranged orderly, symmetrical when installing the vertical and horizontal center lines should be on the same line, deviation is less than 5mm. (9) the emergency lighting installation: according to the design and specifications to determine location of evacuation lighting, signs should