1.- Resolver los siguientes triángu a) \( \begin{array}{l}\alpha=37^{\circ} 24^{\prime} 36^{\prime \prime} \\ c=4,1 \mathrm{~m} .\end{array} \) \[ \]

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

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

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

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