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

1 Answer
Jim H
Apr 15, 2015

cos^-1(-1/4) is a t in [0, pi] with cos t = -1/4

Since t is in quadrant 1 or 2, sint is positive.

The problem becomes: cost=-1/4 and sint >0. Find sint.

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^2t+cos^2 = 1 to get

sint = sqrt15/4

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