Find the exact value of each expression if it is defined If

Find the exact value of each expression, if it is defined. (If an answer does not exist, enter DNE.)

Solution

a) tan^-1(1)

y = tan^-1(1)

tany = pi/4

y= pi/4

b) cos^-1(sqrt3/2)

y =cos^-1(sqrt3/2)

cosy = sqrt3/2

So, y = pi/6

c) tan^-1(tan9pi)

y =  tan^-1(tan9pi)

tany = tan(9pi)

y = 9pi

d) cos( tan^-1(-sqrt3) )

Let y = tan^-1(-sqrt3)

tany = -sqrt3

cosy = 1/2

y = cos^-1(1/2)

cos( tan^-1(-sqrt3) ) = cos(cos^-1(1/2)) = 1/2