Give the exact value of each of the following: csc 5π/6

Question

anonymous · Answer

ok
you have the 

$$csc\frac{5pi}{6}$$
or 
$$5*\pi=5*180=900$$
$$5\pi/6=900/6=150$$
so you need to find 
$$\csc(150)$$

anonymous · Answer

$$csc(150)=csc(90+60)$$
$$csc(90+60)=sec(60)$$
$$sec(60)=2$$

anonymous · Answer

I do the same thing with this problem: sec 5π/6

anonymous · Answer

Lol why do you do that?
Let a = 5Pi/6 so I don't have to type as much
csc a = (sin a)^-1
csc a = (sin Pi/6)^-1 since sine is the same for the angle Pi/6 and 5Pi/6.
 = (1/2)^-1 = 2

For sec a,
sec a = (cos a)^-1
sec a = -(cos Pi/6)^-1 since cosine is the negative for the two angles
sec a = (1/sqrt3)^-1
sec a = - sqrt 3