Question

find all solutions to the equation.

2cosθ + 1 = 0

write your answer in radians in terms of π, and use the \or\ button as necessary.

example: θ = \frac{π}{5}+2kπ, k ∈ z or θ = \frac{π}{7}+kπ, k ∈ z

θ =

Explanation:

Step1: Solve for \(\cos\theta\)

$$
LATEXBLOCK0
$$

Step2: Find the general solutions

We know that \(\cos\theta =-\frac{1}{2}\) when \(\theta=\frac{2\pi}{3}+2k\pi,k\in\mathbb{Z}\) (in the second quadrant) or \(\theta=\frac{4\pi}{3}+2k\pi,k\in\mathbb{Z}\) (in the third quadrant)

Answer:

\(\theta=\frac{2\pi}{3}+2k\pi,k\in\mathbb{Z}\text{ or }\theta=\frac{4\pi}{3}+2k\pi,k\in\mathbb{Z}\)