How to find the exact values of an equation

Find the EXACT value without using a calculator:

tan(4π/3) = ?
tan(3π/4) = ?
cot(5π/3) = ?
sec(π/3) = ?
csc(5π/6) = ?

3^(1/2)
-1
-1/3^(1/2)
2
2

Use the Unit Circle to get the sine and cosine values of each angle. Then combine them to get the values you need.
tan = sin/cos
cot = cos/sin
sec = 1/cos
csc = 1/sin

For example, look up 4π/3 on the Unit Circle. It says that cos(4π/3) = -1/2 and sin(4π/3) = -√3/2.
tan(4π/3) = sin(4π/3)/cos(4π/3)
= (-√3/2)/(-1/2)
= √3