Give the exact value of each trigonometric expression No dec

Give the exact value of each trigonometric expression. (No decimals.) sin(2 pi/3) cos (pi/6) tan (7 pi/4) sec (- 5 pi/6) Sin^-1(1/2) cos (sin^-1(x))

e. sin^-1(1/2)

sin (pi/6)= 1/2

= sin^-1(sin(pi/6))= pi/6

f. cos (sin^-1x)

let sin^-1 x=t

x= sin t

sin theta = opposite/ hypotenuse

therefore opposite = x and hypotenuse=1

and on using pythagoras theorem we get

adjacent = sqrt (1-x^2)

cos theta= adjacent/ hypotenuse

cos t= sqrt (1-x^2)/1

substituting back sin^-1 x for t, we get

cos(sin^-1(x))= sqrt (1- x^2)