Question

Solve 2cos theta+2=3 in the interval 0-2pi

Answer 1

Answer:

$\theta=\frac{\pi}{3}, \frac{5\pi}{3}$.

Step-by-step explanation:

$2\cos(\theta)+2=3$

Subtract 2 on both sides:

$2\cos(\theta)=3-2$

Simplify:

$2\cos(\theta)=1$

Divide both sides by 2:

$\cos(\theta)=\frac{1}{2}$

Now let's refer to the unit circle... When is the x-coordinate, 1/2?

There are 2 places this happens on [0,2pi].

One is in the first quadrant and the other in the fourth quadrant.

It is at $\theta=\frac{\pi}{3}, \frac{5\pi}{3}$.