Question

Factor the algebraic expression below in terms of a single trigonometric function.

sin²x + sin x-2

Answer 1

`( \sin(x) + 2)( \sin(x) - 1)`

Step-by-step explanation

The given trigonometric function is:

`\sin^(2) x + \sin(x) - 2`

This is a quadratic trinomial in sinx

We split the middle term to obtain:

`\sin^(2) x + 2 \sin(x) - \sin(x) - 2`

`\sin \:x ( \sin(x) + 2 ) - 1( \sin(x) + 2)`

The factors are:

`( \sin(x) + 2)( \sin(x) - 1)`