If $\theta=\frac{-7 \pi}{4}$, then find exact values for the following:
$\sec (\theta)$ equals
$\csc (\theta)$ equals
$\tan (\theta)$ equals
$\cot (\theta)$ equals
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Step 1 ：Recognize that the angle \(\frac{-7 \pi}{4}\) is equivalent to \(\frac{\pi}{4}\) in the unit circle because adding or subtracting \(2\pi\) to an angle doesn't change its position in the unit circle.

Step 2 ：Identify the trigonometric functions for \(\frac{\pi}{4}\): \(\sin(\frac{\pi}{4}) = \cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}\), and \(\tan(\frac{\pi}{4}) = 1\).

Step 3 ：Calculate the secant, cosecant, and cotangent, which are the reciprocals of cosine, sine, and tangent, respectively.

Step 4 ：Final Answer: The exact values for the trigonometric functions are: \(\sec (\theta) = \boxed{\sqrt{2}}\), \(\csc (\theta) = \boxed{\sqrt{2}}\), \(\tan (\theta) = \boxed{1}\), and \(\cot (\theta) = \boxed{1}\).