Question

Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.)
cos(θ) = 1/2

Answer 1

Answer:

That is the solutions are:

$\frac{\pi}{3}+2\pi \cdot k$,$\frac{5\pi}{3}+2\pi \cdot k$

Step-by-step explanation:

The period of $\cos(x)$ or $\sin(x)$ is $2\pi$.

Let's look at the first rotation to see when $\cos(\theta)=\frac{1}{2}$ happens.

This happens at $\frac{\pi}{3}$ and also at $\frac{5\pi}{3}$. (Notice I just looked at the x-coordinates because that is what cosine is. Sine is the y-coordinate.)

Now to find the rest of the solutions we can just make full rotations either way to get back to those points .

That is the solutions are:

$\frac{\pi}{3}+2\pi \cdot k$

$\frac{5\pi}{3}+2\pi \cdot k$