How do you find the exact value of sin (x/2) and cos (x/2) if cos x= - 1/4 and pi< x<2pi

Patricia Bean 2022-07-21 Answered
How do you find the exact value of sin ( x 2 ) and cos ( x 2 ) if cos x = 1 4 and π < x < 2 π?
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Answers (1)

autarhie6i
Answered 2022-07-22 Author has 18 answers
Use the trig identity: cos x = 1 2 sin 2 ( x 2 )
1 4 = 1 2 sin 2 ( x 2 ) sin 2 ( x 2 ) = 5 8 = 0.625
sin x / 2 = 0.79
Next, use trig identity: cos 2 ( x 2 ) sin 2 ( x 2 ) = cos x
cos 2 ( x 2 ) = 1 4 + 5 8 = 3 8 cos x 2 = 0.61
Check
sin 2 ( x 2 ) + cos 2 ( x 2 ) = 5 8 + 3 8 = 8 8 = 1
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