Question

find all solutions to the equation.
2cos0 + 1 = 0
write your answer in radians in terms of π, and use the \or\ button as necessary.
example: 0 = \frac{π}{5}+2kπ,k∈z or 0 = \frac{π}{7}+kπ,k∈z
0 = □

Explanation:

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

$$
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$$

We know that \(\cos\theta =-\frac{1}{2}\). The general solution of \(\cos\theta = \cos\alpha\) is \(\theta = 2k\pi\pm\alpha,k\in\mathbb{Z}\). Since \(\cos\frac{2\pi}{3}=-\frac{1}{2}\)

Step2: Find the general solutions

The solutions of \(\cos\theta=-\frac{1}{2}\) are \(\theta = 2k\pi\pm\frac{2\pi}{3},k\in\mathbb{Z}\)

Answer:

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