# All solutions for trig equation

• Sep 13th 2011, 05:18 AM
terrorsquid
All solutions for trig equation
Find all solutions for each of the following in ther given intervals:

$\displaystyle (a) tan^2(x) = 3,~ -2\pi<x\le\pi$

$\displaystyle (b) sin^2(x) = \frac{1}{2},~ \frac{\pi}{2}\le x\le2\pi$

(a)

$\displaystyle tan(x) = \sqrt3$

Do I find only the values that are positive $\displaystyle \sqrt{3}$ in the given interval? i.e., $\displaystyle \frac{\pi}{3}$, $\displaystyle -\frac{2\pi}{3}$, $\displaystyle -\frac{5\pi}{3}$ or do I just find every value where $\displaystyle tan(x) = \sqrt3$?, i.e, 60, 180-60, -60, -180-(-60), -180+(-60), -360-(-60)

(b)

same deal accept with $\displaystyle \frac{\pi}{4}$
• Sep 13th 2011, 05:45 AM
Prove It
Re: All solutions for trig equation
Quote:

Originally Posted by terrorsquid
Find all solutions for each of the following in ther given intervals:

$\displaystyle (a) tan^2(x) = 3,~ -2\pi<x\le\pi$

$\displaystyle (b) sin^2(x) = \frac{1}{2},~ \frac{\pi}{2}\le x\le2\pi$

(a)

$\displaystyle tan(x) = \sqrt3$

Do I find only the values that are positive $\displaystyle \sqrt{3}$ in the given interval? i.e., $\displaystyle \frac{\pi}{3}$, $\displaystyle -\frac{2\pi}{3}$, $\displaystyle -\frac{5\pi}{3}$ or do I just find every value where $\displaystyle tan(x) = \sqrt3$?, i.e, 60, 180-60, -60, -180-(-60), -180+(-60), -360-(-60)

(b)

same deal accept with $\displaystyle \frac{\pi}{4}$

Well first of all $\displaystyle \displaystyle \tan^2{x} = 3 \implies \tan{x} = \pm \sqrt{3}$, not $\displaystyle \displaystyle \sqrt{3}$...
• Sep 13th 2011, 05:52 AM
terrorsquid
Re: All solutions for trig equation
(Doh) ah ok, thanks. So it is everything.