1、诱导公式第三课时 练习1.cos-203=(). A.12 B.32 C.-12 D.-322.(多选题)下列三角函数值与sin3的值相同的是().A.sinn+43 B.cos2n+6C.sin2n+3 D.cos(2n+1)-63.已知2,若cos6-=-34,则sin+56的值为().A.-34 B.34C.-134 D.1344.已知,0,2,且,的终边关于直线y=x对称,若sin =35,则sin =().A.35 B.45 C.7210 D.33+42105.已知3sin+2+sin(+)=0,(-,0),则sin =().A.-31010 B.-1010C.31010 D.101
2、06.已知a=tan-76,b=cos 234,c=sin-334,则b+c=;a,b,c的大小关系是.7.已知是第四象限角,且tan =-2,计算下列各式的值:(1)3sin2-5sin2+-cos2+;(2)sin(-)cos(+)+3cos2.8.(多选题)已知sin(540-x)tan(900-x)1tan(450-x)tan(810-x)cos(360-x)sin(-x),则().A.当x=120时,上式的值为32B.当x=150时,上式的值为12C.当x=240时,上式的值为32D.当x=-60时,上式的值为-329.已知tan =2,则sin2-+3cos(+)sin(-)+co
3、s32+=.10.已知0,2,且tan2-tan -2=0.(1)求tan 的值;(2)求sin2+-sin(-)cos(-)+2sin(+)的值.11.在平面直角坐标系中,以坐标原点为顶点,以x轴的非负半轴为角的始边,已知角的终边与单位圆交于点A-35,45,角的终边落在射线y=x(x0)上.(1)求sin tan 的值;(2)求sin2-sin(3+)+sin232-sin2+3sincos的值.12.在4sin(2021-)=3cos(2021+),sin +cos =15,的终边关于x轴对称,并且4sin =3cos 这三个条件中任选一个,补充在下面问题中.已知第四象限角满足,求下列各
4、式的值.(1)3sin+4coscos-sin;(2)sin2+3sin cos .参考答案1.C2.BC3.C4.B5.A6.0bac7.【解析】(1)3sin2-5sin2+-cos2+=3cos5cos+sin=35+tan=35+(-2)=1.(2)由tan =sincos=-2,得sin =-2cos ,则sin2+cos2=(-2cos )2+cos2=5cos2=1,因为是第四象限角, 所以cos =55,sin =-255, 所以sin(-)cos(+)+3cos2=-sin cos +3cos2=25555+3552=25+35=1.8.ABD9.-1210.【解析】(1)由
5、题意可得(tan -2)(tan +1)=0,tan =2或tan =-1,又0,2,tan 0,tan =2.(2)原式=cos-sincos-2sin=1-tan1-2tan=13.11.【解析】(1)依题意,点A到原点O的距离为452+-352=1,由三角函数的定义知sin =45,设射线y=x(x0)上任意一点为B(m,m),m0,则tan =mm=1,所以sin tan =45.(2)(法一)由三角函数的定义知,tan =-43,tan =1,故sin2-sin(3+)+sin232-sin2+3sincos=-cossin+cos2sin2+3sincos=-1tan+1tan2+
6、3tan=34+14=1.(法二)由三角函数的定义知,sin =45,cos =-35,sin =22,cos =22,故sin2-sin(3+)+sin232-sin2+3sincos=-cossin+cos2sin2+3sincos=34+14=1. 12.【解析】选,4sin(2021-)=3cos(2021+),4sin =-3cos ,tan =-34.选,是第四象限角,sin 0,又sin +cos =15,15-cos2+cos2=1,cos =45,sin =-35,tan =-34.选,是第四象限角,sin 0,又,的终边关于x轴对称,sin =-sin ,cos =cos ,又4sin =3cos ,-4sin =3cos ,即tan =-34.(1)3sin+4coscos-sin=3tan+41-tan=-94+41+34=1.(2)sin2+3sin cos =sin2+3sincossin2+cos2=tan2+3tantan2+1=-2725.
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