If cos 60° = 1/2, which of the following angle has cosine of -1/2?
Answer Details
Let's use the fact that cosine is an even function, meaning that cos(-x) = cos(x). Therefore, we can find the angle with cosine of -1/2 by finding the angle with cosine of 1/2 and then taking its negative.
We know that cos(60°) = 1/2. The cosine function is positive in the first and fourth quadrants, so we need to look for angles in those quadrants where cos(x) = 1/2.
In the first quadrant, the reference angle for which cosine is 1/2 is 60°. In the fourth quadrant, the reference angle is 360° - 60° = 300°.
Taking the negative of these reference angles, we get that the angles with cosine of -1/2 are:
- 60° - 180° = -120°
- 300° - 180° = 120°
Therefore, the answer is 120°.