求y=sin(2x-30度)cos2x的值域.

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求y=sin(2x-30度)cos2x的值域.
求y=sin(2x-30度)cos2x的值域.

求y=sin(2x-30度)cos2x的值域.
y=sin(2x-30度)cos2x的值域:-3/4≤y≤1/4
y=sin(2x-30°)cos2x
=[sin(2x-30°+2x)+sin(2x-30°-2x)]/2
=[sin(4x-30°)-sin30°]/2
=[sin(4x-30°)-1/2]/2
-1≤sin(4x-30°)≤1
y=[sin(4x-30°)-1/2]/2
4y+1=2sin(4x-30°)
sin(4x-30°)=(4y+1)/2
-1≤(4y+1)/2≤1
-3/4≤y≤1/4

积化和差sinXcosY=1/2[sin(X+Y)+sin(X-Y)]
cosXsinY=1/2[sin(X+Y)-sin(X-Y)]
用这个公式就可以了.
y=sin(2x-30度)cos2x=1/2[sin(4x-30)+sin(-30)]
而sinx 的值域应该知道吧