Indicate the signs of \( \tan \theta \) if the terminal side of angle \( \theta \) (with the initial side in the standard position) is in the Fourth Quadrant.

Three trigonometric functions for a given angle are shown below. \( \sin \theta=-\frac{77}{85}, \cos \theta=\frac{36}{85}, \tan \theta=-\frac{77}{36} \) What are the coordinates of point \( (x, y) \) on the terminal ray of angle \( \theta \), assuming that the values above were not simplified? \( (-77,-36) \) \( (-77,36) \) \( (-36,77) \) \( (36,-77) \)

Based on Pythagorean identities, which equation is true? \( \begin{array}{l}\sin ^{2} \theta-1=\cos ^{2} \theta \\ \sec ^{2} \theta-\tan ^{2} \theta=-1 \\ -\cos ^{2} \theta-1=-\sin ^{2} \theta \\ \cot ^{2} \theta-\csc ^{2} \theta=-1\end{array} \)

Which Pythagorean identity is correct? \( \begin{array}{l}\sin ^{2}(\theta)+1=\cos ^{2}(\theta) \\ \tan ^{2}(\theta)+1=\sec ^{2}(\theta) \\ 1-\cot ^{2}(\theta)=\csc ^{2}(\theta) \\ 1-\cos ^{2}(\theta)=\tan ^{2}(\theta)\end{array} \)

The point \( \left(-\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right) \) is the point at which the terminal ray of angle \( \theta \) intersects the unit circle. What are the values for the \( \operatorname{cosine} \) and cotangent functions for angle \( \theta \) ? \( \cos \theta=-\frac{\sqrt{2}}{2}, \cot \theta=-1 \) \( \cos \theta=\frac{\sqrt{2}}{2}, \cot \theta=1 \) \( \cos \theta=\frac{\sqrt{2}}{2}, \cot \theta=-\frac{1}{2} \) \( \cos \theta=-\frac{\sqrt{2}}{2}, \cot \theta=\frac{1}{2} \)

If \( \tan \theta=-\frac{3}{8} \), which expression is equivalent to \( \cot \theta ? \) \( \frac{1}{-\frac{3}{8}} \) \( -\frac{3}{8}+1 \) \( \sqrt{1+\left(-\frac{\theta}{3}\right)^{2}} \) \( \left(-\frac{3}{8}\right)^{2}+1 \)