课时分层作业4 单位圆与正弦函数、余弦函数的基本性质单位圆的对称性与诱导公式.doc

课时分层作业(四)单位圆与正弦函数、余弦函数的基本性质单位圆的对称性与诱导公式(建议用时：40分钟)[学业达标练]一、选择题1．cos660°的值为()A．－eq\f(12)B.eq\f(12)C．－eq\f(\r(3)2)D.eq\f(\r(3)2)B[cos660°＝cos(360°＋300°)＝cos300°＝cos(180°＋120°)＝－cos120°＝－cos(180°－60°)＝cos60°＝eq\f(12).]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(\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).]4．若cos(2π－α)＝eq\f(\r(5)3)则sineq\b\lc\(\rc\)(\a\vs4\al\co1(\f(3π2)－α))等于()A．－eq\f(\r(5)3)B．－eq\f(23)C．eq\f(\r(5)3)D．±eq\f(\r(5)3)A[∵cos(2π－α)＝cos(－α)＝cosα＝eq\f(\r(5)3)∴sineq\b\lc\(\rc\)(\a\vs4\al\co1(\f(3π2)－α))＝－cosα＝－eq\f(\r(5)3).]5．coseq\b\lc\(\rc\)(\a\vs4\al\co1(kπ＋\f(π3)))(k∈Z)的值为()A．±eq\f(12)B.eq\f(12)C．－eq\f(12)D．±eq\f(\r(3)2)A[若k为偶数不妨设k＝2n(n∈Z)则coseq\b\lc\(\rc\)(\a\vs4\al\co1(kπ＋\f(π3)))＝coseq\b\lc\(\rc\)(\a\vs4\al\co1(2nπ＋\f(π3)))＝coseq\f(π3)＝eq\f(12)；若k为奇数可设k＝2n＋1(n∈Z)则coseq\b\lc\(\rc\)(\a\vs4\al\co1(kπ＋\f(π3)))＝coseq\b\lc\(\rc\)(\a\vs4\al\co1(2nπ＋π＋\f(π3)))＝coseq\b\lc\(\rc\)(\a\vs4\al\co1(π＋\f(π3)))＝－coseq\f(π3)＝－eq\f(12).综上coseq\b\lc\(\rc\)(\a\vs4\al\co1(kπ＋\f(π3)))的值为±eq\f(12).]二、填空题6．函数y＝2－sinx的最小正周期为________．[解析]因为2－sin(2π＋x)＝2－sinx所以y＝2－sinx的最小正周期为2π.[答案]2π7．若coseq\b\lc\(\rc\)(\a\vs4\al\co1(\f(π2)＋θ))＋sin(π＋θ)＝－m则coseq\b\lc\(\rc\)(\a\vs4\al\co1(\f(3π2)－θ))＋2sin(6π－θ)＝________.【导学号：64012025】[解析]∵coseq\b\lc\(\rc\)(\a\vs4\al\co1(\f(π2)＋θ))＋sin(π＋θ)＝－sinθ＋(－sinθ)＝－2sinθ＝－m∴sinθ＝eq\f(m2).∴coseq\b\lc\(\rc\)(\a\