19) Find \( \sin A \) and \( \cot B \) for a right triangle given that \( b=2, c=\sqrt{29} \). a) \( \sin A=\frac{\sqrt{29}}{5}, \cot B=\frac{2}{5} \) b) \( \sin A=\frac{5 \sqrt{29}}{29}, \cot B=\frac{5}{2} \) c) \( \sin A=\frac{2}{5}, \cot B=\frac{5}{2} \) d) \( O \sin A=\frac{5}{29}, \cot B=\frac{5}{2} \)

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 \( \theta \) ? \( \cos \theta=-\frac{\sqrt{2}}{2}, \cot \theta=-1 \) \( \cos \theta=\frac{\sqrt{2}}{2}, \cot \theta=1 \) \( \cos \theta=\frac{\sqrt{2}}{2}, \cot \theta=-\frac{1}{2} \) \( \cos \theta=-\frac{\sqrt{2}}{2}, \cot \theta=\frac{1}{2} \)

The point \( P(x, y) \) lies on the terminal side of an angle \( \theta=\frac{3 \pi}{4} \) in standard position. What are the signs of the values of \( x \) and \( y \) ? Both \( x \) and \( y \) are positive. Both \( x \) and \( y \) are negative. \( x \) is positive, and \( y \) is negative. \( x \) is negative, and \( y \) is positive.

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

If \( \sin \theta \) s -0.7660 , which of the following represents an approximate value of \( \tan \theta \), for \( 180^{\circ}<\theta<270^{\circ} \) ? 0.7660 0.8392 1.1916 1.4198

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? \( (-77,-36) \) \( (-77,36) \) \( (-36,77) \) \( (36,-77) \)