Question

Solve each of the following for the given domain. State your answers by using the

indicated units. a. cos 𝜃 =−√3/2, −180° ≤ 𝜃 ≤ 360°

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve for 𝜃, we need to find the angles in the given domain where cos 𝜃 = -√3/2.

Since cos 𝜃 = -√3/2 is negative, we are dealing with angles in the second and third quadrants where cosine is negative.

First, let's find the reference angle whose cosine is √3/2. We know that cos 30° = √3/2, so the reference angle is 30°.

In the second quadrant, cos 𝜃 = -√3/2, so 𝜃 = 180° - 30° = 150°.

In the third quadrant, cos 𝜃 = -√3/2, so 𝜃 = 180° + 30° = 210°.

Therefore, the solutions in the given domain are 𝜃 = 150° and 𝜃 = 210°.