Express the sum as a product. If possible, find this product's exact value. \( \sin 285^{\circ}+\sin 15^{\circ} \) Choose the correct answer below. A. \( \sin 285^{\circ}+\sin 15^{\circ}=2 \sin 300^{\circ} \cos 270^{\circ} \) B. \( \sin 285^{\circ}+\sin 15^{\circ}=2 \cos 150^{\circ} \sin 135^{\circ} \) C. \( \sin 285^{\circ}+\sin 15^{\circ}=2 \sin 150^{\circ} \sin 135^{\circ} \) D. \( \sin 285^{\circ}+\sin 15^{\circ}=2 \sin 300^{\circ} \sin 270^{\circ} \) E. \( \sin 285^{\circ}+\sin 15^{\circ}=2 \cos 300^{\circ} \sin 270^{\circ} \) F. \( \sin 285^{\circ}+\sin 15^{\circ}=2 \sin 150^{\circ} \cos 135^{\circ} \)

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

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 terminal side of an angle in standard position passes through \( P(-3,-4) \). What is the value of \( \tan \theta \) ? \( \tan \theta=-\frac{4}{3} \) \( \tan \theta=-\frac{3}{4} \) \( \tan \theta=\frac{3}{4} \) \( \tan \theta=\frac{4}{3} \)

25. ¿Cuál es una solución de la ecuación trigonométrica \( \sin (x)=1 / 2 \) en el intervalo \( [0,2 \pi] \) ? \( \pi / 8 y 3 \pi / 8 \) \( \pi / 4 y \pi / 2 \) \( \pi / 4 y 3 \pi / 4 \) \( \pi / 8 y \pi / 4 \)

2. Halle el valor numérico de \[ H=2 \cos 180^{\circ} \cdot \sec 360^{\circ} \cdot \csc 270 \] \( \begin{array}{lll}\text { A) }-1 & \text { B) }-2 & \text { C) } 0 \\ \text { D) } 1 & \text { E) } 2 & \end{array} \)