Solve each of the following for the given domain. Express each answer in the indicated
unit value. a. cos 𝜃 =−√3/2, 0° ≤ 𝜃 ≤ 360°
To solve for 𝜃 in the given domain when cos 𝜃 = -√3/2, we need to find the reference angle and determine in which quadrants cosine is negative.
Since cos 𝜃 is negative, we know that 𝜃 is in the second or third quadrant.
The reference angle for cos 𝜃 = -√3/2 is 30° (cosine of 30° is √3/2).
In the second quadrant, the reference angle is 30°, so 𝜃 = 180° - 30° = 150°.
In the third quadrant, the reference angle is 30°, so 𝜃 = 360° - 30° = 330°.
Therefore, the solutions for cos 𝜃 = -√3/2 in the given domain are 𝜃 = 150° and 𝜃 = 330°.