Question #3efc5

2 Answers
Feb 10, 2017

θ = 90°, or 180°, or 270°.

Explanation:

First, we can factor our a 4cosθ to get:

4cosθ(cosθ + 1) = 0

This means that either 4cosθ = 0 => cosθ = 0

or cosθ + 1 = 0 => cosθ = -1

You can consult the trigonometric circle below to help:

graph{x^2 +y^2 = 1 [-2.5, 2.5, -1.25, 1.25]}

cosθ corresponds to the x axis. The angle θ is measured from the Ox semiaxis, going counterclockwise. Therefore,

cosθ = 0 => θ = 90° or θ = 270°
cosθ = -1 => θ = 180°

So the three possible solutions are

{90°, 180°, 270°}

Feb 10, 2017

theta = 90^o, 180^o and 270^o

Explanation:

Factor: 4cos theta (cos theta + 1) = 0

4 cos theta = 0, and cos theta = -1

From a trig. circle: cos theta = 0 occurs at 90^o and 270^o
From a trig. circle: cos theta = -1 occurs at 180^o