三角函数
若f(x)=asin(x+四分之派)+3sin(x-四分之派)是偶函数,则a=???
∵ f(x)=asin(x+π/4)+3sin(x-π/4)是偶函数, ∴ asin(x+π/4)+3sin(x-π/4)=asin(-x+π/4)+3sin(-x-π/4) asin(x+π/4)+3sin(x-π/4)=-asin(x-π/4)-3sin(x+π/4) (a+3)[sin(x+π/4)+sin(x-π/4)]=0 (a+3)·2√2sin(2x)cos(π/4)=0 2(a+3)sin(2x)=0与x无关 ∴ a=3=0, a=-3
答:因为f(sinx)=3-cos2x 所以fcosx)=f(sin(pi/2-x)) 函数式中的cosx应该归结为sinX, =3-cos[2(pi/2-x)...详情>>
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