find the exact value of expression: sin( tan^-1(-radical11/radical5)-cos^-1(radical3/2))

Answer 1

easier than it looks:

cos^-1(radical3/2), means you want the angle Ø
so that cosØ = √3/2
of course you should recognize that as a ratio form our 30-60-90 triangle, and Ø = 30°

for tan^-1 (-√11/√5), construct a triangle in quadrant II so that tanß = -√11/√5
use your calculator to find ß = 180° - 56.012°
= 123.988°

so we have sin(123.988 - 30)
= appr .9976