91Ó°ÊÓ

Sketch the graph of \(y=2 \sin x\) from \(x=0\) to \(x=2 \pi\) by making a table using multiples of \(\pi / 2\) for \(x\). What is the amplitude of the graph you obtain?

\(y=2+\sin x\)

Use a calculator to evaluate each expression to the nearest tenth of a degree. \(\sin ^{-1}(-0.1702)\)

In Chapters 2 and 3, we worked some problems involving the Ferris wheel called Colossus that was built in St. Louis in 1986. The diameter of the wheel is 165 feet, it rotates at \(1.5\) revolutions per minute, and the bottom of the wheel is 9 feet above the ground. Find an equation that gives a passenger's height above the ground at any time \(t\) during the ride. Assume the passenger starts the ride at the bottom of the wheel.

\(y=-3+\sin \left(\pi x+\frac{\pi}{2}\right)\)

Use your graphing calculator to graph \(y=\sin ^{-1} x\) in degree mode. Use the graph with the appropriate command to evaluate each expression. a. \(\sin ^{-1}\left(-\frac{1}{2}\right)\) b. \(\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)\) c. \(\arcsin \left(-\frac{1}{\sqrt{2}}\right)\)

Prove each identity. \(\sin (-\theta) \sec (-\theta) \cot (-\theta)=1\)

A point is moving with an angular velocity of 3 radians per second on a circle of radius 6 meters. How far does the point travel in 10 seconds?

Graph one complete cycle for each of the following. In each case, label the axes accurately and state the period and phase shift for each graph. $$ y=\cot \left(x+\frac{\pi}{4}\right) $$

Use your calculator to find \(\theta\) to the nearest tenth of a degree if \(0^{\circ}<\theta<360^{\circ}\) and\(\cos \theta=0.7455\) with \(\theta\) in QIV