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To find the secant of angle $\theta$, we start by recalling that $\sec(\theta) = \frac{1}{\cos(\theta)}$.

Let’s consider an angle $\theta = \frac{5\pi}{4}$.

First, we find $\cos(\frac{5\pi}{4})$:

$\cos(\frac{5\pi}{4}) = -\frac{\sqrt{2}}{2}$

Thus, $\sec(\frac{5\pi}{4}) = \frac{1}{-\frac{\sqrt{2}}{2}} = -\sqrt{2}$

Therefore, $\sec(\frac{5\pi}{4}) = -\sqrt{2}$

To find the secant of $ heta$, remember that $sec( heta) = frac{1}{cos( heta)}$.

Consider the angle $ heta = frac{7pi}{6}$.

We calculate $cos(frac{7pi}{6})$:

$cos(frac{7pi}{6}) = -frac{sqrt{3}}{2}$

Therefore, $sec(frac{7pi}{6}) = frac{1}{-frac{sqrt{3}}{2}} = -frac{2}{sqrt{3}} = -frac{2sqrt{3}}{3}$

Hence, $sec(frac{7pi}{6}) = -frac{2sqrt{3}}{3}$

Recall that $sec( heta) = frac{1}{cos( heta)}$.

For angle $ heta = frac{3pi}{2}$:

$cos(frac{3pi}{2}) = 0$

Hence, $sec(frac{3pi}{2})$ is undefined as division by zero is not possible.

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