27. REASONING Determine whether you would use a sine or cosine function to model each sinusoid with the \( y \)-intercept described. Explain your reasoning. a. The \( y \)-intercept occurs at the maximum value of the function. b. The \( y \)-intercept occurs at the minimum value of the function. c. The \( y \)-intercept occurs halfway between the maximum and minimum values of the function.

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.

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

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

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

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