Question

Problem Solving
Find the exact solution of each equation for 0 < theta < 2 pi

Answer 1

Answer:

C) $\theta=\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$

Step-by-step explanation:

$sin^2\theta=\frac{1}{2},\: 0\leq\theta\leq2\pi\\ \\\frac{1-cos(2\theta)}{2}=\frac{1}{2}\\ \\1-cos(2\theta)=1\\\\cos(2\theta)=0\\\\2\theta=\frac{\pi}{2}+\pi n\\ \\\theta=\frac{\pi}{4}+\frac{\pi}{2}n\\ \\ \theta=\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$

Recall the identity $sin^2\theta=\frac{1-cos(2\theta)}{2}$