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# Find the exact value. $\csc \frac{9 \pi}{4}$

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$\csc \dfrac{9\pi}{4}$

To find the value of any trigonometric function for any angle $\theta$, we first find the reference angle $\overline{\theta}$ associated with the angle $\theta$. The reference angle is the acute angle formed by the terminal side of the angle $\dfrac{9\pi}{4}$ and the $x$-axis.

The above angle can be written as

$\dfrac{9\pi}{4} = 2\pi + \dfrac{\pi}{4}$

Since, the terminal side of this angle is in Quadrant I, the reference angle will be the angle itself. Since, the sign of cosecant function is positive in the Quadrant I, the value of $\csc \dfrac{9\pi}{4}$ is

$\csc \dfrac{9\pi}{4} = \csc \dfrac{\pi}{4} = \sqrt{2}$

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