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课时作业7诱导公式与旋转[练基础]1.如果cos(π+A)=-12,那么sinπ2+A等于()A.-12B.12C.-32D.322.下列式子与sinθ-π2相等的是()A.sinπ2+θB.cosπ2+θC.c
os32π-θD.sin32π+θ3.若sin(π-α)=-13,那么cos3π2-α的值为()A.13B.-13C.223D.-2234.若sinπ2-α=35,cosπ2+α=45,则sinπ2+
α-cos(π-α)sinπ2+α-sin(3π-α)等于()A.1B.-1C.67D.-675.求值:cosπ5+cos2π5+cos3π5+cos4π5=________.6.(1)求值:cos3π2+π3+sin-100π3(2)化简:co
s5π2+αcos(α-π)+2sin(3π-α)sinπ2+α2sin(4π-α)cos(5π+α)[提能力]7.[多选题]若角A,B,C是△ABC的三个内角,则下列等式中不成立的是()A.cos(A+B)=cosCB.sin(A+B)=-sinCC.cosA+
C2=sinBD.sinB+C2=cosA28.已知角α的终边在直线y=x上,则sin3π2-αsin(3π-α)=________.9.已知4cosα-sinα3sinα+2cosα=14,求cos
3π2-αcos(-3π+α).[战疑难]10.已知f(x)=sinπx(x<0),f(x-1)-1(x>0),则f-116+f116的值为()A.3B.-3C.2D.-2