Find the following values without a calculator a tan tan16

Find the following values, without a calculator: (a) tan (tan^-1(6)) = (b) sin^-1 (sin (7 pi/6) = c) Sin (tan^-1 (x/4) =

Solution

a. tan(tan^-1theta)=theta

b. sin^-1(sin(7pi/6))= sin^-1(sin(-pi/6))=-pi/6

c. sin(tan^-1(x/4))

tan^-1(x/4)=y

tan y=x/4

sin y=x/sqrt(x²+16)

sin(tan^-1(x/4)) =x/sqrt(x²+16)