SOLUTION: How do I find the exact ratio of sec pi/6?

Question 285662: How do I find the exact ratio of sec pi/6?
Found 2 solutions by Alan3354, nerdybill:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
It's a value.
If you're allowed to start with the cosine, it's
sec(pi/6) = 1/cos(pi/6) = 1/(sqrt(3)/2)
=

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
How do I find the exact ratio of sec pi/6?
.
You find the exact value by applying identities and the "unit circle".
.
From identities:
sec(pi/6) = 1/cos(pi/6)
.
But, from the unit circle we know that cos(pi/6) is sqrt(3)/2
therefore:
sec(pi/6) = 1/cos(pi/6)
sec(pi/6) = 1/[sqrt(3)/2]
sec(pi/6) = 2/sqrt(3)
.
Now we "rationalize" (remove sqrt from denominator):
sec(pi/6) = 2/sqrt(3) * sqrt(3)/sqrt(3)
sec(pi/6) = 2sqrt(3)/3 (this is your exact value)

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