How do you evaluate $csc((5pi)/3)$ ?

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Answer 1 · 2016-08-01T17:22:40

Let's first convert to degrees, which I personally find easier to work with. Use the conversion factor $180/pi$ .

$(5pi)/3 xx 180/pi$

$=300˚$

Recall that $csctheta = 1/sintheta$ , so $csc300˚ = 1/(sin300˚)$ .

The reference angle for $300˚$ is $60˚ -> sin60˚ = sqrt(3)/2$ . Since $300˚$ is in quadrant IV, $sin$ is negative, so $sin300˚ = -sqrt(3)/2$ .

However, since $csc300˚ = 1/(sin300˚)$ , $csc300˚ = 1/(sqrt(3)/2) = 2/sqrt(3) = (2sqrt(3))/3$ .

Hopefully this helps!

How do you evaluate csc((5pi)/3)csc((5pi)/3)?