Question

What is the range of `cos^2x+2sinx-2`?

Answer 1

Numerical value of `cos^2x+2sinx-2=-(1-sinx)^2` ranges from `[-4,0]`.

Explanation:

`cos^2x+2sinx-2`

= `1-sin^2x+2sinx-2`

= `-(1-2sinx+sin^2x)`

= `-(1-sinx)^2`

As `sinx` ranges from `[-1,1]`, `cos^2x+2sinx-2` or `-(1-sinx)^2` ranges from `[-4,0]`.

graph{(cosx)^2+2sinx-2 [-10.46, 9.54, -7.2, 2.8]}