find the exact value of the expression sincos1211 costan115S

find the exact value of the expression

sin(cos^-1(-2/11)

cos(tan^-1(-1/5)

Solution

sin(cos^-1(-2/11))

let cos^-1(-2/11)=t

cos t=-2/11

here hypotenuse=11 and adjacent=2

opposite=sqrt(121-4)=sqrt117

sin t=sqrt117/11

sin(cos^-1(-2/11)=sqrt117/11=3sqrt13/11