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Math Help - Finding the Exact Value of an Inverse Trigonometry Function

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    Finding the Exact Value of an Inverse Trigonometry Function

    Hello,

    I want to find the exact value of  csc(-\frac{5\pi}{3})
    I know that  csc(\theta)=\frac{1}{sin(\theta)}, and the answer to the question is  \frac{2\sqrt{3}}{3} , but don't know how this works!

    Thank you for your answers!
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    Re: Finding the Exact Value of an Inverse Trigonometry Function

    Quote Originally Posted by ianm View Post
    Hello,

    I want to find the exact value of  csc(-\frac{5\pi}{3})
    I know that  csc(\theta)=\frac{1}{sin(\theta)}, and the answer to the question is  \frac{2\sqrt{3}}{3} , but don't know how this works!

    Thank you for your answers!
    \displaystyle \begin{align*} \csc{\left( -\frac{5\pi}{3} \right)} &= \frac{1}{\sin{\left( -\frac{5\pi}{3} \right)}} \\ &= \frac{1}{\sin{\left( \frac{\pi}{3} \right)}} \textrm{ since } \sin{\left( \theta + 2\pi \right)} = \sin{(\theta)} \\ &= \frac{1}{\frac{\sqrt{3}}{2}} \\ &= \frac{2}{\sqrt{3}} \\ &= \frac{2\sqrt{3}}{3} \end{align*}
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