How to find the exact values of cos(5pi/12) using the half angle formula?

Alyssa Hanson

Alyssa Hanson

Answered question

2023-03-18

How to find the exact values of cos(5pi/12) using the half angle formula?

Answer & Explanation

Krasiniecb8rw

Krasiniecb8rw

Beginner2023-03-19Added 7 answers

Using the formula for a half-angle:
XXXX cos ( θ 2 ) = ± 1 + cos ( θ ) 2
If θ 2 = 5 π 12
XXXX then θ = 5 π 6
Note that 5 π 6 is a standard angle in quadrant 2 with a reference angle of π 6
so cos ( 5 π 6 ) = - cos ( π 6 ) = - 3 2
Therefore
XXXX cos ( 5 π 12 ) = ± 1 - 3 2 2
XXXXXXXXXXX = ± 2 - 3 2 2
XXXXXXXXXXX = ± 2 - 3 4
XXXXXXXXXXX = ± 2 - 3 2
Since 5 π 12 < π 2
XXXX 5 π 12 is in quadrant 1
XXXX cos ( 5 π 12 ) is positive
XXXX (the negative solution is extraneous)

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