# Thread: Exact Values and Trigonometric Equations

1. ## Exact Values and Trigonometric Equations

Determine all the possible values of x where 0 degree <= x <= 360 degree such that

sec^2 x + sec x = 2

2. ## Re: Exact Values and Trigonometric Equations

Hey choi105.

Can you show us what you have tried?

3. ## Re: Exact Values and Trigonometric Equations

sec^2 x + sec x = 2
(sec x - 1)( sec x + 2) = 0
sec x - 1 = 0 or sec x + 2 = 0
sec x = 1 or sec x = -2
1/cos x = 1 or 1/cos x = -2

then i don't know how to continue...

4. ## Re: Exact Values and Trigonometric Equations

There are exact values for +-1/2 and +-1. (Hint Consider pi/2, pi/3 and 2pi/3)

5. ## Re: Exact Values and Trigonometric Equations

Originally Posted by choi105
sec^2 x + sec x = 2
(sec x - 1)( sec x + 2) = 0
sec x - 1 = 0 or sec x + 2 = 0
sec x = 1 or sec x = -2
1/cos x = 1 or 1/cos x = -2

then i don't know how to continue...
Surely you can see where $\displaystyle \cos{(x)} = 1$ and $\displaystyle \cos{(x)} = -\frac{1}{2}$...