How to find the exact values of cos 15 using the half angle formula?

Shirley Peck

Shirley Peck

Answered question

2023-03-24

How to find the exact values of cos 15 using the half angle formula?

Answer & Explanation

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coguarsbq2q

Beginner2023-03-25Added 10 answers

The formula for the cosine half-angle
cos ( x 2 ) = ± 1 + cos x 2
The sign is positive if x 2 is in the first or fourth quadrant and negative if x 2 is in the second or third quadrant.

15 ° is in the first quadrant, so the sign is positive.
15 = 30 2

cos 15 = cos ( 30 2 ) = 1 + cos 30 2
cos 15 = 1 + 3 2 2 = 2 + 3 4
cos 15 = 2 + 3 2

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