SOLUTION: csc -13(pie) _______ 3

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Question 789117: csc -13(pie)
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3
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
csc%28-13pi%2F3%29=csc%28-12pi%2F3-pi%2F3%29=csc%28-4pi-pi%2F3%29=csc%28-pi%2F3%29
That is because -13pi%2F3=-12pi%2F3-pi%2F3-4pi-pi%2F3
The added -4pi angle is 2 clockwise turns, so the -pi%2F3 and -4pi-pi%2F3 angles are coterminal angles, indistinguishable from each other unless you are watching the turns.
(Shaun White may say there is a big difference between a {{-60^o}}} and a -720%5Eo-60%5Eo=-780%5Eo, but the turns end in the same position, and the values of the trigonometric functions are the same.

Next csc%28-pi%2F3%29=1%2Fsin%28-pi%2F3%29
and sin%28-pi%2F3%29=-sin%28pi%2F3%29=-sqrt%283%29%2F2
So csc%28-13pi%2F3%29=1%2F%28-sqrt%283%29%2F2%29=-2%2Fsqrt%283%29=-2sqrt%283%29%2F2