Answer: cos 20 = -√3/2
Explanation:
Since sin 2015 = 0 and 20° is in the second quadrant, we know that the reference angle for 20° is 20° - 180° = -160°. So we need to find the value of cos(-160°).
We can use the fact that cos(-θ) = cos(θ) to find the value of cos(-160°) as follows:
cos(-160°) = cos(160°)
To find the cosine of 160°, we can use the identity cos(180° - θ) = -cos(θ) as follows:
cos(160°) = cos(180° - 20°) = -cos(20°)
Now, we need to determine the sign of cos(20°) in the second quadrant. Since 30°, 45° and 60° are angles in the first quadrant with exact values of √3/2 and 90° - 60° = 30°, 90° - 45° = 45°, 90° - 30° = 60° are their respective corresponding angles in the second quadrant, we can use the fact that cosine is a decreasing function in the second quadrant to conclude that:
1 > cos(20°) > √3/2
Therefore, since sin 2015 = 0, we know that cos(-160°) = -cos(20°) = 0, which implies that cos(20°) = 0.
Therefore, cos 20 = -√3/2.