Question

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

Answer 1

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
\[\csc(150)\]

Answer 2

\[csc(150)=csc(90+60)\]
\[csc(90+60)=sec(60)\]
\[sec(60)=2\]

Answer 3

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

Answer 4

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