Asked by Ansley

sin [sin -1 (7/25) - cos -1 (-8/17)]
Answered by Reiny
let A = sin^-1 (7/25)
then cosA = 24/25 ---> sinA = 7/25

let B = cos^-1 (-8/17)
cosB = --8/17 , let's assume B is in II
sin B = 15/17

so sin [sin -1 (7/25) - cos -1 (-8/17)]
= sin (A - B)
= sinAcosB - cosAsinB
= (7/25)(-8/17) - (24/25)(15/17)
= (-56 - 360)/425
<b>= -416/425</b>

check with calculator:
A = 16.26°
B = 118.07°
A-B = -101.81°
sin(-101.81°) = -.9788
-416/425 = -.9788 , how about that?
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