# What are the solutions to the equation sin^2x+cosx=-1 on the interval 0 ≤ x < 2pi?

##### 2 Answers

#### Explanation:

To solve an equation like this, it is helpful to have only one trig function so we can solve for it and then solve for

First, we can use the Pythagorean identity

Let

Rearranging this into quadratic form we get

Since

#### Explanation:

Replace sin^2 x by

(cos x)(- cos x +1) = 0

Either one of the factors should be zero.

a. cos x = 0 --> Unit circle gives 2 solutions:

b. - cos x + 1 = 0 --> cos x = 1

x = 0 and

Answers for interval

Note: 2pi is not included in the solution set -->