How to find the exact values of cos(11pi/12) using the half angle formula?

chururiakop

chururiakop

Answered question

2023-03-11

How to find the exact values of cos(11pi/12) using the half angle formula?

Answer & Explanation

Metafune7re

Metafune7re

Beginner2023-03-12Added 2 answers

Call cos ( 11 π 12 ) = cos t
cos 2 t = cos ( 22 π 12 ) = cos ( 11 π 6 ) = cos ( π 6 ) = 3 2
Put the trig identity to use: cos 2 t = 2 cos 2 t - 1
cos 2 t = 3 2 = 2 cos 2 t - 1
2 cos 2 t = 1 + 3 2 = 2 + 3 2
cos 2 t = 2 + 3 4
cos t = cos ( 11 π 12 ) = ± 2 + 3 2 .
Since the arc ((11pi)/12) is located in Quadrant II, only the negative answer is accepted.
cos ( 11 π 12 ) = - 2 + 3 2
Check by calculator.
A r c ( 11 π 12 ) = 165 deg-> cos ( 11 π 12 ) = cos 165 = - 0.97 .
- ( 2 + 3 2 ) = - 0.97 .

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