# Thread: Find solutions for this equation in the intervals given:

1. ## Find solutions for this equation in the intervals given:

Find all solutions for each of the following equations in the intervals given:
a)$\displaystyle sin^2x = \frac{1}{4}, \frac{\pi}{2}<=x<2\pi;$

b)$\displaystyle tan^2x = 1, {-\pi}<=x<\pi;$

how would i attack these questions? if you could explain i would really appreciate it. thank u

2. Originally Posted by jvignacio
Find all solutions for each of the following equations in the intervals given:
a)$\displaystyle sin^2x = \frac{1}{4}, \frac{\pi}{2}<=x<2\pi;$

b)$\displaystyle tan^2x = 1, {-\pi}<=x<\pi;$

how would i attack these questions? if you could explain i would really appreciate it. thank u
a) $\displaystyle \sin^2{x} - \frac{1}{4} = 0$

$\displaystyle \left(\sin{x} + \frac{1}{2}\right)\left(\sin{x} - \frac{1}{2}\right) = 0$

$\displaystyle \sin{x} = -\frac{1}{2}$ ... $\displaystyle x = \frac{7\pi}{6}$ ... $\displaystyle x = \frac{11\pi}{6}$

$\displaystyle \sin{x} = \frac{1}{2}$ ... $\displaystyle x = \frac{5\pi}{6}$

b) $\displaystyle \tan^2{x} - 1 = 0$

finish up by factoring ... you should get $\displaystyle x = \pm \frac{\pi}{4}$ and $\displaystyle x = \pm \frac{3\pi}{4}$