trigonometry hw help

Question

Find the exact value of cot(8π/3) and the reference angle. 

Reference angle (in radians):    Write your answer in terms of π by typing pi.

cot(8π/3)=  _______  Do not use decimals.

Answer 1

8pi/3 has same trig functions as 2pi/3. 8pi/3-2pi = 8pi/3-6pi/3 = (8-6)pi/3 = 2pi/3

cot(8pi/3) = cot(2pi/3) = -1/sqr3= -sqr3/3

Answer 2

So we can convert 8pi/3 into degrees by multiplying by pi/180:

8pi/3 * 180/pi = 60 * 8 = 480.

This is outside of the unit circle so we can subtract 360 (the degrees of a circle) to find an angle coterminal to it.

480 - 360 = 120

Now we can evaluate cos(120) by looking at a unit circle!

Remember, unit circle is (cos,sin)