How to find the value of sin (22 1/2) using the double or half angle formula?

Laney Bradley

Laney Bradley

Answered question

2023-01-26

How to find the value of sin ( 22 1 2 ) using the double or half angle formula?

Answer & Explanation

Gerardo Goodman

Gerardo Goodman

Beginner2023-01-27Added 7 answers

Use trig identity:
2 sin 2 a = 1 - cos 2 a
In this case, a = ( 22 5 ) and 2 a = 45 -->
2 sin 2 ( 22.5 ) = 1 - cos 45 = 1 - 2 2 = 2 - 2 2
sin 2 ( 22.5 ) = 2 - 2 4
sin ( 22.5 ) = ± 2 - 2 2
Take the positive value since sin (22.5) is a positive number.
sin ( 22.5 ) = 2 - 2 2

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