How to use the half-angle identity to find the exact value of cos (11pi/8)?

Dylan Chandler

Dylan Chandler

Answered question

2023-03-11

How to use the half-angle identity to find the exact value of cos (11pi/8)?

Answer & Explanation

Bronchialyo2

Bronchialyo2

Beginner2023-03-12Added 7 answers

cos ( 11 π 8 ) = cos ( 3 π 8 + π ) = - cos ( 3 π ) 8 = cos t
employ trig identity cos 2 t = 2 cos 2 t - 1
cos 2 t = cos ( 6 π 8 ) = cos ( 3 π 4 ) = - 2 2
- 2 2 = 2 cos 2 t - 1
2 cos 2 t = 1 - 2 2 = 2 - 2 2
cos 2 t = 2 - 2 4
cos t = cos ( 11 π 8 ) = ± 2 - 2 2 .
Only the negative answer is accepted because the arc (11pi/8 is in Quadrant II.
cos ( 11 π 8 ) = - 2 - 2 2
Check by calculator.
cos ( 11 π 8 ) = cos 247.5 deg = - 0.382
- 2 - 2 2 = - 0.382.

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