24) What is the period of the function : \( f(x)=\frac{-2}{3} \cos \left(\frac{\pi}{4}+4 x\right) \) a) \( 2 \pi \) b) \( \frac{3 \pi}{2} \) c) \( \pi \) d) \( \frac{\pi}{2} \)

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

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

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

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