How do you find the exact value of #csc((17pi)/6)#?

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How do you find the exact value of #csc((17pi)/6)#?

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Answer 1 · 2018-01-23T15:19:33

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Explanation:

First find the angle coterminal to #(17pi)/6# that falls between #0# and #2pi#: #(17pi)/6-2pi=(5pi)/6#. So we know that #csc((17pi)/6) = csc((5pi)/6)#.

#csc(x)=1/sin(x)# and we know that #sin((5pi)/6) = 1/2# because it's from the Unit Circle.

So:

#csc((17pi)/6) = csc((5pi)/6) = 1/sin((5pi)/6) = 1/(1/2)=2#.

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How do you find the exact value of #csc((17pi)/6)#?

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