Question

Find all solutions of the equation in the interval [0, 2pi).

Answer 1

Answer:

$\displaystyle \theta=\frac{\pi}{4}, \frac{3\pi}{4}$

Step-by-step explanation:

We want to find the solutions to:

$2\sin(\theta)-\sqrt{2}=0$

Within the interval [0, 2π).

First, isolate the sine:

$\displaystyle \sin(\theta)=\frac{\sqrt{2}}{2}$

Recall the unit circle. This is true twice: at π/4 and 3π/4.

Hence, our solutions are:

$\displaystyle \theta=\frac{\pi}{4}, \frac{3\pi}{4}$