Evaluate the following expression without a calculator Be su

Evaluate the following expression without a calculator. Be sure to rationalize denominators, where appropriate. Sin (cos^-1 - 5/7)

Solution

Sin(cos^-1-5/7)

Let cos^-1(-5/7) = t

cos t=-5/7

Adjacent=5 and hypotenuse=7

Opposite=sqrt(49-25) =2sqrt6

Sin t=2sqrt6/7

Sin(cos^-1(-5/7))=2(sqrt6 )/7