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.
c. Calculate the values of 𝜃 in standard position.

Answer 1

a. The cosine function is negative in the second and third quadrants, so the terminal arm could be located in either of those quadrants.

b. Diagram:

```
^
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2nd c |_________► 3rd c
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<------------------------>
180° 360°
```

c. To find the values of 𝜃 in standard position where cos 𝜃 = -1/2, we can look at the unit circle.

The cosine function is equal to -1/2 at 120° and 240°. So, 𝜃 could be 120° and 240° in this case.