How do you find the exact value fo sin (cos^-1 (-1/4))

kjukks1234531 2022-09-17 Answered
How do you find the exact value for sin ( cos 1 ( 1 4 ) )?
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Answers (1)

Zackary Galloway
Answered 2022-09-18 Author has 17 answers
cos 1 ( 1 4 ) is a t in [ 0 , π ] with cos t = 1 4
Since t is in quadrant 1 or 2, sin t is positive.
The problem becomes: cos t = 1 4 and sin t > 0. Find sin t.
Either draw a picture of t on the coordinate system,
or draw a right triangle with acute angle t, adjacent side 1 and hypotenuse 4
or use sin 2 t + cos 2 = 1 to get
sin t = 15 4

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