PAGE課時素養(yǎng)檢測四十四誘導(dǎo)公式(一)(30分鐘60分)一、選擇題(每小題5分,共30分)1.cos150°= ()A.QUOTE B.QUOTE C.-QUOTE D.-QUOTE【解析】選D.由誘導(dǎo)公式可得cos150°=cosQUOTE=-cos30°=-QUOTE.【補(bǔ)償訓(xùn)練】tan300°= ()A.QUOTEB.-QUOTEC.QUOTED.-QUOTE【解析】選B.tan300°=tan(360°-60°)=tan(-60°)=-tan60°=-QUOTE.2.cosQUOTE+sinQUOTE的值為 ()A.-QUOTE B.QUOTEC.QUOTE D.QUOTE【解析】選C.原式=cosQUOTE-sinQUOTE=cosQUOTE-sinQUOTE=-cosQUOTE+sinQUOTE=QUOTE.3.已知sin(π+α)=QUOTE,α為第三象限角,則cos(π-α)= ()A.QUOTE B.-QUOTE C.QUOTE D.-QUOTE【解析】選A.因為sin(π+α)=QUOTE,所以sinα=-QUOTE.因為α為第三象限角,所以cosα=-QUOTE.所以cos(π-α)=-cosα=QUOTE.4.化簡QUOTE= ()A.sin2+cos2 B.sin2-cos2C.cos2-sin2 D.±(cos2-sin2)【解析】選A.依據(jù)誘導(dǎo)公式,化簡QUOTE=QUOTE=QUOTE,又因為sin2>0,且QUOTE>QUOTE,所以QUOTE=sin2+cos2.5.已知sin(π+θ)=-QUOTEcos(2π-θ),|θ|<QUOTE,則θ等于 ()A.-QUOTE B.-QUOTE C.QUOTE D.QUOTE【解析】選D.由sin(π+θ)=-QUOTEcos(2π-θ),|θ|<QUOTE,可得-sinθ=-QUOTEcosθ,|θ|<QUOTE,即tanθ=QUOTE,|θ|<QUOTE,所以θ=QUOTE.6.設(shè)角α=-QUOTEπ,則QUOTE的值等于 ()A.QUOTE B.-QUOTE C.QUOTE D.-QUOTE【解析】選A.QUOTE=QUOTE=QUOTE=QUOTE=QUOTE=QUOTE.因為α=-QUOTEπ,所以tanα=tanQUOTE=tanQUOTE=tanQUOTE=QUOTE,原式=QUOTE=QUOTE.二、填空題(每小題5分,共10分)7.下列三角函數(shù),其中n∈Z:①sinQUOTE;②cosQUOTE;③sinQUOTE;④cosQUOTE,其中與sinQUOTE的值相同的是______(填序號).

【解析】sinQUOTE=QUOTEcosQUOTE=cosQUOTE=sinQUOTE;sinQUOTE=sinQUOTE;cosQUOTE=cosQUOTE,所以應(yīng)填②③.答案:②③8.若cosQUOTE=QUOTE,則cosQUOTE=________.

【解析】cosQUOTE=cosQUOTE=-cosQUOTE=-QUOTE.答案:-QUOTE三、解答題(每小題10分,共20分)9.已知sin(α+π)=QUOTE,且sinαcosα<0,求QUOTE的值.【解析】因為sin(α+π)=QUOTE,所以sinα=-QUOTE,又因為sinαcosα<0,所以cosα>0,cosα=QUOTE=QUOTE,所以tanα=-QUOTE.所以原式=QUOTE=QUOTE=-QUOTE.10.化簡:cosQUOTE+cosQUOTE(n∈Z).【解析】原式=cosQUOTE+cosQUOTE.(1)當(dāng)n為奇數(shù),即n=2k+1(k∈Z)時,原式=cosQUOTE+cosQUOTE=-cosQUOTE-cosQUOTE=-2cos