Explain how to solve these please 37 an4 csc tan 1V3 cos1 S

37 an(4 csc - tan 1(-V3) cos-1 Sin-1 V3 Here is a unit circle you can use if you want to

Solution

tan(5 pi/4)

Here theta is in third quadrant where tan is positive

Therefore tan (5pi/4)=1

csc(11pi/3)

Here theta is in fourth quadrant where sin and csc are negative

Therefore csc(11pi/3)=-2/sqrt3

tan^-1(-sqrt 3) =tan^-1(tan(-pi/3)) = -pi/3

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

sin^-1(-sqrt 3/2) = sin^-1(sin(-pi/3))= -pi/3