2024-2025學(xué)年高中數(shù)學(xué)第一章三角函數(shù)1.3三角函數(shù)的誘導(dǎo)公式二課時(shí)素養(yǎng)評價(jià)含解析新人教A版必修4

PAGE三角函數(shù)的誘導(dǎo)公式(二)(15分鐘30分)1.若角α的終邊過點(diǎn)A(2,1),則sinQUOTE= ()A.QUOTE B.-QUOTE C.QUOTE D.-QUOTE【解析】選B.sinQUOTE=-cosα,又α的終邊過A(2,1),所以cosα=QUOTE,故sinQUOTE=-QUOTE.【補(bǔ)償訓(xùn)練】已知sinA=QUOTE,那么cosQUOTE= ()A.-QUOTE B.QUOTEC.-QUOTE D.QUOTE【解析】選A.cosQUOTE=-sinA=-QUOTE.2.已知sinQUOTE=QUOTE,則cosQUOTE的值為 ()A.QUOTE B.-QUOTE C.QUOTE D.-QUOTE【解析】選C.cosQUOTE=cosQUOTE=sinQUOTE=QUOTE.3.已知α∈QUOTE,且cosα=-QUOTE,則sinQUOTE·tanQUOTE= ()A.-QUOTE B.QUOTE C.-QUOTE D.QUOTE【解析】選D.sinQUOTE·tanQUOTE=cosα·tanα=sinα,因?yàn)棣痢蔘UOTE,且cosα=-QUOTE,所以sinα=QUOTE=QUOTE=QUOTE.4.已知cosQUOTE=QUOTE,則cosQUOTE·sinQUOTE-α的值為.

【解析】方法一:cosQUOTE·sinQUOTE=cosQUOTE·sinQUOTE=-cosQUOTE·sinQUOTE=-QUOTEsinQUOTE=-QUOTEcosQUOTE=-QUOTE.方法二:原式=cosQUOTEsinQUOTE=-cosQUOTEcosQUOTE=-QUOTE.答案:-QUOTE5.已知α是第三象限角,且cosα=-QUOTE.(1)求tanα的值.(2)化簡并求QUOTE的值.【解析】(1)由題意得,α是第三象限的角,所以sinα=-QUOTE=-QUOTE,所以tanα=QUOTE=3.(2)原式=QUOTE=QUOTE=QUOTE,當(dāng)tanα=3時(shí),原式=QUOTE=QUOTE.(20分鐘40分)一、選擇題(每小題5分,共20分)1.若f(sinx)=3-cos2x,則f(cosx)= ()A.3-cos2x B.3-sin2xC.3+cos2x D.3+sin2x【解析】選C.f(cosx)=fQUOTE=3-cos(π-2x)=3+cos2x.2.已知sinQUOTE=-QUOTE,則cosQUOTE= ()A.QUOTE B.-QUOTE C.QUOTE D.-QUOTE【解析】選A.sinQUOTE=sinQUOTE=-sinQUOTE=-QUOTE,所以sinQUOTE=QUOTE,故cosQUOTE=cosQUOTE=sinQUOTE=QUOTE.3.已知cosQUOTE=-QUOTE,則sinQUOTE的值等于 ()A.QUOTE B.QUOTE C.-QUOTE D.-QUOTE【解析】選B.sinQUOTE=sinQUOTE,=-sinQUOTE=-cosQUOTE=QUOTE.4.已知QUOTE=2,則sin(α-5π)·sinQUOTE= ()A.QUOTE B.QUOTE C.±QUOTE D.-QUOTE【解析】選B.已知QUOTE=2,故tanα=3,又sin(α-5π)·sinQUOTE=-sinαQUOTE=QUOTE,故原式=QUOTE=QUOTE.二、填空題(每小題5分,共10分)5.已知tan(3π+α)=2,則QUOTE=.

【解析】由tan(3π+α)=2,得tanα=2,則原式=QUOTE=QUOTE=QUOTE=QUOTE=QUOTE=2.答案:26.若sinQUOTE=QUOTE,則sinQUOTE=,

sin2QUOTE=.

【解析】因?yàn)閟inQUOTE=QUOTE,所以sinQUOTE=sinQUOTE=sinQUOTE=QUOTE,sin2QUOTE=sin2QUOTE=cos2QUOTE=1-sin2QUOTE