# How do you solve #2cos^2 theta - cos theta -1 = 0#?

##### 2 Answers

As you can see, this is a quadratic equation in cosine. It can be solved by factoring.

As you probably know, trinomials of the form

Factor out a common factor from both pairs of binomials (encased in the parentheses). Note that when you're fully competent at this task the parentheses are unnecessary. For this case, they were just used to focus your attention.

By special angles:

Hopefully this helps!

#### Explanation:

Solve the quadratic equation for cos t.

Since a + b + c = 0, use shortcut. The 2 real roots are:

cos t = 1 and

Trig table and unit circle -->

a. cos t = 1 --> arc

b.

The arc

Answers for (0, 2pi):