find the exact value of the expressions whenever they are de

find the exact value of the expressions whenever they are defined. Do not round.

Solution

a) sin^-1(-sqrt3/2)

y =sin^-1(-sqrt3/2)

siny = -sqrt(3)/2

range of sin^-1x is [ -pi/2 , pi/2]

y = sin^-1(-sqrt3/2) =  -pi/3

b) cos^-(-1/2)

y =cos^-(-1/2)

range of cos^-1x is [0, pi]

cosy = -1/2

y = pi-pi/3 = 2pi/3

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