Which of the following could be found in a table of values for the function \( g(x)=\cos (-1.5 x)-1 ? \) (1 point) \( \left(\frac{2 \pi}{3}, 0\right) \) There is no viable option provided. \( \left(\frac{2 \pi}{3},-1\right) \) \( \left(\frac{2 \pi}{3},-2\right) \)

What is the period of \( y=\sin (3 x) \) ? \( \begin{array}{l}\frac{\pi}{3} \\ \frac{2 \pi}{3} \\ 3 \pi \\ 6 \pi\end{array} \)

Starting at its rightmost position, it takes 2 seconds for the pendulum of a grandfather clock to swing a horizontal distance of 18 inches from right to left and 2 seconds for the pendulum to swing back from left to right. Which of the following equations models \( d \), the horizontal distance in inches of the pendulum from the center as a function of time, \( t \), in seconds? Assume that right of center is a positive distance and left of center is a negative distance. \( d=9 \cos \left(\frac{\pi}{4} t\right) \) \( d=9 \cos \left(\frac{\pi}{2} t\right) \) \( d=18 \cos \left(\frac{\pi}{4} t\right) \) \( d=18 \cos \left(\frac{\pi}{2} t\right) \)

Prove the following trigonometric identity: \( \frac{\sin A\left[1-\sin \left(360^{\circ}-A\right)\right]}{1-\cos ^{2}\left(180^{\circ}+A\right)}-1=\operatorname{cosec} A \)

Which transformations are needed to change the parent cosine function to \( y=3 \cos (10(x-\pi)) \) ? vertical compression of 3 , horizontal stretch to a period of \( 5 \pi \), phase shift of \( \pi \) units to the left vertical stretch of 3 , horizontal compression to a period of \( \frac{\pi}{5} \), phase shift of \( \pi \) units to the right vertical compression of 3 , horizontal stretch to a period of 10 p, phase shift of \( \pi \) units to the right vertrech of 3 , horizontal compression to a period of \( \frac{\pi}{5} \), phase shift of \( \pi \) units to the left

5. Se observa un semáforo desde la ventana de un edificio, a 30 m del suelo. El ángulo de depresión para observar la parte superior del semáforo es de \( 70^{\circ} \), mientras que el ángulo de depresión para observar su base mide \( 88^{\circ} \). ¿Cuál es la altura del semáforo?