2020_2021学年新教材高中数学第一章三角函数1.doc

课时分层作业(五)诱导公式与对称诱导公式与旋转(建议用时：40分钟)一、选择题1．已知sineq\b\lc\(\rc\)(\a\vs4\al\co1(α－\f(π4)))＝eq\f(13)则coseq\b\lc\(\rc\)(\a\vs4\al\co1(α＋\f(π4)))的值等于()A．－eq\f(13)B．eq\f(13)C．－eq\f(2\r(2)3)D．eq\f(2\r(2)3)A[coseq\b\lc\(\rc\)(\a\vs4\al\co1(α＋\f(π4)))＝sineq\b\lc\[\rc\](\a\vs4\al\co1(\f(π2)－\b\lc\(\rc\)(\a\vs4\al\co1(α＋\f(π4)))))＝sineq\b\lc\(\rc\)(\a\vs4\al\co1(\f(π4)－α))＝－sineq\b\lc\(\rc\)(\a\vs4\al\co1(α－\f(π4)))＝－eq\f(13).]2．若sin(θ＋π)<0cos(θ－π)>0则θ在()A．第一象限B．第二象限C．第三象限D．第四象限B[∵sin(θ＋π)＝－sinθ<0∴sinθ>0.∵cos(θ－π)＝cos(π－θ)＝－cosθ>0∴cosθ<0∴θ为第二象限角．]3．已知sineq\b\lc\(\rc\)(\a\vs4\al\co1(α－\f(π6)))＝eq\f(13)则coseq\b\lc\(\rc\)(\a\vs4\al\co1(α＋\f(π3)))的值为()A．－eq\f(2\r(3)3)B．eq\f(2\r(3)3)C．eq\f(13)D．－eq\f(13)D[coseq\b\lc\(\rc\)(\a\vs4\al\co1(α＋\f(π3)))＝coseq\b\lc\[\rc\](\a\vs4\al\co1(\f(π2)＋\b\lc\(\rc\)(\a\vs4\al\co1(α－\f(π6)))))＝－sineq\b\lc\(\rc\)(\a\vs4\al\co1(α－\f(π6)))＝－eq\f(13).]4．若sin(π＋α)＋coseq\b\lc\(\rc\)(\a\vs4\al\co1(\f(π2)＋α))＝－m则coseq\b\lc\(\rc\)(\a\vs4\al\co1(\f(3π2)－α))＋2sin(2π－α)的值为()A．－eq\f(2m3)B．eq\f(2m3)C．－eq\f(3m2)D．eq\f(3m2)C[∵sin(π＋α)＋coseq\b\lc\(\rc\)(\a\vs4\al\co1(\f(π2)＋α))＝－sinα－sinα＝－m∴sinα＝eq\f(m2).故coseq\b\lc\(\rc\)(\a\vs4\al\co1(\f(3π2)－α))＋2sin(2π－α)＝－sinα－2sinα＝－3sinα＝－eq\f(32)m.]5．已知sineq\b\lc\(\rc\)(\a\vs4\al\co1(\f(5π4)＋α))＝eq\f(\r(3)2)则sineq\b\lc\(\rc\)(\a\vs4\al\co1(\f(3π4)－α))的值为()A．eq\f(12)B．－eq\f(12)C．eq\f(\r(3)2)D．－eq\f(\r(3)2)D[sineq\b\lc\(\rc\)(\a\vs4\al\co1(\f(3π4)－α))＝sineq\b\lc\[\rc\](\a\vs4\al\co1(π－\b\lc\(\rc\)(\a\vs4\al\co1(\f(3π4)－α))))＝sineq\b\lc\(\rc\)(\a\vs4\al\co1(\f(π4)＋α))＝－sineq\b\lc\(\rc\)(\a\vs4\al\co1(\f(5π4)＋α))＝－eq\f(\r(3)2).]二、填空题6．cos660°＝________.eq\f(12)[cos660°＝cos(360°＋300°)＝cos300°＝cos(180°＋120°)＝－cos120°＝－cos(180°－60°)＝cos60°＝eq\f(12).]7．cos1°＋cos2°＋cos3°＋…＋cos179°＋cos180°＝________.－1[cos179°