Question

求y=sin(2x-30度)cos2x的值域.

Answer 1

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