Use a sketch to find the exact value of the expression tansi

Use a sketch to find the exact value of the expression tan(sin^-1(square root 2/2).

Find the exact value of the expression cos^-1 (-square root 3/2).

Solution

given expression tan(sin^-1(square root 2/2).

                            sqrt(2) / 2 = 1/sqrt(2)

                             from the sketch of grpah sin45 = 1/sqrt(2)

   so the expression becomes tan(45)

but tan45=1

2)

cos^-1 (-square root 3/2).

now cos^-1(-x) = -cos^-1(x)

                          = -cos^-1(sqrt(3) /2)

                         = - pi/6