Answer:
120° & 240° (given the angles are between 0° and 360°)
Explanation:
We want to find
.
This means we want to know the angle(s) for which cosine has a value of
.
The basic acute angle that has a cosine of
is 60°. But we want to know NEGATIVE
. So in which quadrants is cosine negative? Second and Third
- The rule to find 2nd quadrant angle with known acute angle is: 180 - α
- The rule to find 3rd quadrant angle with known acute angle is: 180 + α
Where α is the basic acute angle (in our case it is 60°)
So 2nd quadrant angle is 180 - 60 = 120°
and 3rd quadrant angle is 180 + 60 = 240°