1、1.2.4诱导公式(二)一、选择题1.已知cos ,则sin等于()A. B. C. D.答案A解析sincos .2.已知sin 10k,则cos 620的值为()A.k B.k C.k D.不确定答案B解析cos 620cos(360260)cos 260cos(27010)sin 10k.3.已知sin,则cos等于()A. B. C. D.答案B解析因为sin,所以coscossin.4.已知sin,则cos的值等于()A. B.C. D.答案A解析cossinsinsin.5.若sin(3),则cos等于()A. B. C. D.答案A解析sin(3)sin ,sin .coscos
2、cossin .6.已知cos(75),则sin(15)cos(105)的值是()A. B. C. D.答案D解析sin(15)cos(105)sin(75)90cos180(75)sin90(75)cos(75)cos(75)cos(75)2cos(75).7.若sin()cosm,则cos2sin(2)的值为()A. B. C. D.答案C解析sin()cossin sin m,sin .故cos2sin(2)sin 2sin 3sin .8.已知为锐角,2tan()3cos5,tan()6sin()1,则sin 等于()A. B.C. D.答案C解析由题意,得解得tan 3,又为锐角,s
3、in2cos21,可得sin .二、填空题9.若cos ,且是第四象限角,则cos .答案解析cos ,且是第四象限角,sin .cossin .10.sin21sin22sin288sin289 .答案解析原式(sin21sin289)(sin22sin288)(sin244sin246)sin24544.11.化简: .答案1解析原式1.三、解答题12.已知角的终边经过点P(4,3),求的值.解角的终边经过点P(4,3),tan ,tan .13.已知sincos,且cos 0,即sin cos 0,sin cos 0,sin cos ,sin cos ,得sin ,得cos .14.给出
4、下列三个结论,其中正确结论的序号是 .sin()sin 成立的条件是角是锐角;若cos(n)(nZ),则cos ;若(kZ),则tan.答案解析由诱导公式三,知R时,sin()sin ,所以错误.当n2k(kZ)时,cos(n)cos()cos ,此时cos ,当n2k1(kZ)时,cos(n)cos(2k1)cos()cos ,此时cos ,所以错误.若(kZ),则tan,所以正确.15.化简:sincos (kZ).解原式sincos.当k为奇数时,设k2n1(nZ),则原式sincossincossinsincossinsin0;当k为偶数时,设k2n(nZ),则原式sincossincossincossinsin0.综上所述,原式0.