Question

Find all solutions of the equation in the interval [0, 2π). 2cosθ+ 1= 0

Answer 1

Hello!

$\large\boxed{\frac{2\pi}{3} \text{ and } \frac{4\pi}{3}}$

2cosФ + 1 = 0

Begin by isolating for cosФ. Subtract both sides by -1:

2cosФ = -1

Divide both sides by 2:

cosФ = -1/2

Using the unit circle, we know that from [0, 2π), values that have a cosine of -1/2 are 2π/3 and 4π/3.

Therefore, the solutions of this equation are:

Ф = 2π/3 and 4π/3