these are two separate questions Cas Ecos E40 Solutioncoscos

these are two separate questions.

Solution

cos(-cos^-1(-40))

Let cos^-1(-40)=t

cos(-cos^-1(-40))= cos -t=cos t

cos^-1(-40)=t

cos t=-40

Therefore cos(-cos^-1(-40))=-40

sin(cos^-1(2/3))

let cos^-1(2/3)=t

therefore cos t= 2/3

Here adjacent =2   and hypotenuse=3

Therefore opposite=sqrt(hypotenuse²-adjacent²)= sqrt5

sin t= opposite/hypotenuse= (sqrt5)/3

Hence sin(cos^-1(2/3))= (sqrt5)/3