Find the exact value of each trigonometric functions given N

Find the exact value of each trigonometric functions given. No calculator.

a. cos 7pi/6

b. csc 11pi/3

c. sec 4pi

d. cot -pi/3

a. cos 7pi/6 = cos (pi + pi/6)

And cos (pi+theta)= -cos theta

So cos (pi + pi/6)=- cos pi/6=-sqrt3/2

b. csc 11pi/3

csc theta=1/sin theta

csc 11pi/3=1/sin(11pi/3)= 1/sin(4pi-pi/3)

sin (2pi n - theta)=-sin theta

therefore 1/sin(4pi - pi/3)=1/-sin(pi/3)= -2sqrt3/3

c. sec 4pi=1/cos 4pi=1/1=1

d. cot(-pi/3)=1/tan(-pi/3)= -sqrt3/3