9. a. If cos 𝜃 −1/2, 0° ≤ 𝜃 ≤ 360°, in which quadrants could the terminal arm be located?

Question

b. Draw a labeled diagram to show each case.

Answer 1

a. Since cos 𝜃 is negative, the terminal arm could be located in either Quadrant II or Quadrant III.

b.

Quadrant II:
In Quadrant II, the cosine function is negative. Let's draw a unit circle and mark the angle 𝜃 such that cos 𝜃 = -1/2. Using our understanding of the cosine function, we know that the x-coordinate of the point where the terminal arm intersects the unit circle will be -1/2.

Quadrant III:
Similarly, in Quadrant III, the cosine function is also negative. Therefore, the terminal arm could also be located in Quadrant III. Let's draw a diagram to show this case as well.

(Insert diagram here)