Answer:
π, 7π/6, 3π/4, 4π/3, 3π/2, 5π/3, 7π/4, 2π
Explanation:
You want the angles listed in increasing order of their cosines:
3π/4, π, 7π/6, 5π/3, 7π/4, 4π/3, 3π/2, 2π
Cosine
The cosine function is increasing for angles between π and 2π, so angles in that range will be listed in order of their angle value.
However, the cosine of angles less than π are equivalent to the cosine of the same angle subtracted from 2π. That is, cos(3π/4) = cos(5π/4).
Order
As a multiple of π/12, the given angles are ...
9, 12, 14, 20, 21, 16, 18, 24
where 9π/12 has a cosine equivalent to the cosine of 15π/12. Arranging these values in increasing order, we get ...
12, 14, 15(9), 16, 18, 20, 21, 24
So, the angles in order of increasing cosines are ...
π, 7π/6, 3π/4, 4π/3, 3π/2, 5π/3, 7π/4, 2π
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