Express the given sum as a product of sines and/or cosines. \[ \cos \frac{x}{2}+\cos \frac{3 x}{2} \] \( \cos \frac{x}{2}+\cos \frac{3 x}{2}=\square \) (Simplify your answer.)

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

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 \( \sin \theta \) 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

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.

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