What is arccos \( \left(\frac{\sqrt{2}}{2}\right) \) in radians? You can use the letter \( p \) to indicate pi.

8. The teminal amm for angle \( \theta \) passes through the point \( (7,-6) \). a) Determine the exact simplified ralues of the 6 trigonometric ratios, inolube a diagram.

A buoy starts at a height of 0 in relation to sea level and then goes up. Its maximum displacement in either direction is 6 feet, and the time it takes to go from its highest point to its lowest point is 4 seconds. Which of the following equations can be used to model \( h \), the height in feet of the buoy in relation to sea level as a function of time, \( t \), in seconds? \( h=4 \sin \left(\frac{\pi}{6} t\right) \) \( h=4 \sin \left(\frac{\pi}{3} t\right) \) \( h=6 \sin \left(\frac{\pi}{4} t\right) \) \( h=6 \sin \left(\frac{\pi}{2} t\right) \)

What is the general equation of a cosine function with an amplitude of 3 , a period of \( 4 \pi \), and a horizontal shift of \( -\pi \) ? \( \begin{array}{l}y=4 \pi \cos (3(x-\pi)) \\ y=3 \cos (4 \pi(x+\pi)) \\ y=3 \cos (0.5(x+\pi)) \\ y=4 \pi \cos (0.2(x+\pi))\end{array} \)

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

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