91Ó°ÊÓ

Use the unit circle to evaluate the six trigonometric functions of \(\theta\). \(\theta=-270^{\circ}\)

Identify the amplitude and period of the function. Then graph the function and describe the graph of \(g\) as a transformation of the graph of its parent function. \(g(x)=3 \sin x\)

Sketch the angle. Then find its reference angle. \(320^{\circ}\)

ERROR ANALYSIS Describe and correct the error in fi nding the vertical shift of a sinusoid with a maximum point at (3, ?2) and a minimum point at (7, ?8).

Sketch the angle. Then find its reference angle. \(-370^{\circ}\)

The motion of a pendulum can be modeled by the function \(d=4 \cos 8 \pi t\), where \(d\) is the horizontal displacement (in inches) of the pendulum relative to its position at rest and \(t\) is the time (in seconds). Find and interpret the period and amplitude in the context of this situation. Then graph the function.

MODELING WITH MATHEMATICS A circuit has an alternating voltage of 100 volts that peaks every \(0.5\) second. Write a sinusoidal model for the voltage \(V\) as a function of the time \(t\) (in seconds).

A buoy bobs up and down as waves go past. The vertical displacement \(y\) (in feet) of the buoy with respect to sea level can be modeled by \(y=1.75 \cos \frac{\pi}{3} t\), where \(t\) is the time (in seconds). Find and interpret the period and amplitude in the context of the problem. Then graph the function.

\(\tan 31^{\circ}\)

Evaluate the function without using a calculator. \(\cot \left(\frac{-8 \pi}{3}\right)\)