Calculate the following real number: sin9°

gheadarce

gheadarce

Answered question

2022-11-30

Calculate the following real number:
sin 9 °

Answer & Explanation

Chaya Proctor

Chaya Proctor

Beginner2022-12-01Added 10 answers

x=18 then 5x=90 so 2x=90−3x.
sin ( 2 x ) = sin ( 90 3 x ) 2 sin x cos x = cos 3 x 2 sin x cos x = 4 cos 3 x 3 cos x 2 sin x = 4 cos 2 x 3 2 sin x = 4 4 sin 2 x 3 4 sin 2 x + 2 sin x 1 = 0
Solving this quadratic equation, we get
sin x = 1 + 5 4
cos x = 1 sin 2 x = 0.951
cos x = 2 cos 2 x 2 1
cos x 2 = 0.951 + 1 2 = 0.987
Finally, sin x = 2 sin x 2 cos x 2 so that
sin 9 = sin x 2 = sin x 2 cos x 2 = 0.156

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