# Exact Values and Trigonometric Equations

• Apr 15th 2013, 05:38 PM
choi105
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
• Apr 15th 2013, 05:39 PM
chiro
Re: Exact Values and Trigonometric Equations
Hey choi105.

Can you show us what you have tried?
• Apr 15th 2013, 05:53 PM
choi105
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...
• Apr 15th 2013, 06:45 PM
chiro
Re: Exact Values and Trigonometric Equations
There are exact values for +-1/2 and +-1. (Hint Consider pi/2, pi/3 and 2pi/3)
• Apr 15th 2013, 07:05 PM
Prove It
Re: Exact Values and Trigonometric Equations
Quote:

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 $\displaystyle \displaystyle \cos{(x)} = 1$ and $\displaystyle \displaystyle \cos{(x)} = -\frac{1}{2}$...