How to simplify using the half angle formula sin(22^@ 30')?

Elaina Mullen

Elaina Mullen

Answered question

2023-02-11

How to simplify using the half angle formula sin ( 22 o 30 ) ?

Answer & Explanation

Dale Zuniga

Dale Zuniga

Beginner2023-02-12Added 6 answers

Using the half angle formula for sin
| 2 2 sin ( θ 2 ) = ± 1 - cos θ 2 2 2 | ̲ ¯
here θ 2 = 22.5 θ = 45
Only the positive root is necessary because 22.5 is in the first quadrant where sine is positive.
sin ( 22.5 ) = 1 - cos 45 2
X X X X X X X = 1 - 1 2 2
X X X X X X X = 2 - 1 2 2
× × × × x = 2 - 2 4
× × × × x = 2 - 2 2

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