Find solutions for this equation in the intervals given:

**jvignacio** · November 26th 2008, 03:36 AM

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

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

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

**skeeter** · November 26th 2008, 07:23 AM

Originally Posted by jvignacio

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

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

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

a) $\sin^2{x} - \frac{1}{4} = 0$

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

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

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

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

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

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