已知函数f(x)=sin(x+7/4π)+cos(x-3/4π),x属于R,以下步骤中f(β)为什么等于2sinπ/4

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已知函数f(x)=sin(x+7/4π)+cos(x-3/4π),x属于R,以下步骤中f(β)为什么等于2sinπ/4
已知函数f(x)=sin(x+7/4π)+cos(x-3/4π),x属于R,以下步骤中f(β)为什么等于2sinπ/4

已知函数f(x)=sin(x+7/4π)+cos(x-3/4π),x属于R,以下步骤中f(β)为什么等于2sinπ/4
β= π/2
β + 7/4 pπ= 2π+ π/4
β- 3/4 π= -π/4
cos (-π/4) = cos π/4 = sin π/4
sin (2π + π/4) = sin π/4
所以 f(β) = 2 sin π/4

beta = pi/2
beta + 7/4 pi = 2pi + pi/4
beta - 3/4 pi = -pi/4
cos (-pi/4) = cos pi/4 = sin pi/4
sin (2pi + pi/4) = sin pi/4
so f(beta) = 2 sin pi/4

f(x)=sin(x+1/4π-2*π)+cos(x-1/4π-1/2π)
=sin(x-1/4π)+sin(x-1/4π)
=2*sin(x-1/4π)