Find the range y = - 2cos ^ 2x + 2sinx + 3 / 2, X ∈ [- π / 4, π / 4]

Find the range y = - 2cos ^ 2x + 2sinx + 3 / 2, X ∈ [- π / 4, π / 4]

y=-2cos^2x+2sinx+3/2
=-2(1-sin^2x)+2sinx+3/2
=-2sin^2x+2sin^2x-1/2
=-2(sinx-1/2)^2
-π/4