Find an equation for a sinusoidal function that has period \( 2 \pi \), amplitude 1 , and contains the point \( \left(-\frac{\pi}{2},-2\right) \)

\( 37 \sin ( \alpha + \beta ) \cdot \sin ( \alpha - \beta ) = \cos ^ { 2 } \beta - \cos ^ { 2 } \alpha \)

Find the exact values of the six trigonometic functions for the following angle. \[ 330^{\circ} \]

Question 36, 3.4.7 Part 1 of 3 Suppose that point \( P \) is on a circle with radius \( r \), and ray \( O P \) is rotating with angular speed \( \omega \). Complete parts (a) through (c). \( \mathrm{r}=8 \mathrm{~cm}, \omega=\frac{\pi}{8} \) radian per sec, \( t=3 \mathrm{sec} \)

\( 2 \cos ^ { 2 } x - 1 \geq 0 \)

As part of her assignment, Devi has to use her clinometer to measure the height of an office tower \( T A \). From a point \( B \), she observes that angle \( T B A=34^{\circ} \). She then walks 25 m away from the office tower to a point \( C \) and observes that angle \( T C A=26^{\circ} \). Find the height of the sfice tover.