Question

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

Answer 1

C)
`\theta=(\pi)/(4),(3\pi)/(4),(5\pi)/(4),(7\pi)/(4)`

Explanation:

`sin^2\theta=(1)/(2),\: 0\leq\theta\leq2\pi\\ \\(1-cos(2\theta))/(2)=(1)/(2)\\ \\1-cos(2\theta)=1\\\\cos(2\theta)=0\\\\2\theta=(\pi)/(2)+\pi n\\ \\\theta=(\pi)/(4)+(\pi)/(2)n\\ \\ \theta=(\pi)/(4),(3\pi)/(4),(5\pi)/(4),(7\pi)/(4)`

Recall the identity
`sin^2\theta=(1-cos(2\theta))/(2)`