Chapter 9

COMPLETE THE SENTENCE Graphs of sine and cosine functions are called

The shortest repeating portion of the graph of a periodic function is called a(n) ______

COMPLETE THE SENTENCE In a right triangle, the two trigonometric functions of ? that are defi ned using the lengths of the hypotenuse and the side adjacent to ? are __________ and __________.

Write the expression \(\cos 130^{\circ} \cos 40^{\circ}-\sin 130^{\circ} \sin 40^{\circ}\) as the cosine of an angle.

\(\mathrm{A}(\mathrm{n})\) _____ is an angle in standard position whose terminal side lies on an axis.

WRITING Explain why the graphs of the tangent, cotangent, secant, and cosecant functions do not have an

Compare the amplitudes and periods of the functions \(y=\frac{1}{2} \cos x\) and \(y=3 \cos 2 x\).

VOCABULARY Compare an angle of elevation to an angle of depression.

Explain how to evaluate \(\tan 75^{\circ}\) using either the sum or difference formula for tangent.

Given an angle \(\theta\) in standard position with its terminal side in Quadrant III, explain how you can use a reference angle to find \(\cos \theta\).

What is a phase shift? Give an example of a sine function that has a phase shift.

WRITING Explain what it means to solve a right triangle.

In Exercises 3-10, find the exact value of the expression. \(\tan \left(-15^{\circ}\right)\)

\(y=\sin 3 x\)

What is the midline of the graph of the function \(y=2 \sin 3(x+1)-2\) ?

Find the exact value of the expression. \(\tan 195^{\circ}\)

WRITING Explain how to graph a function of the form \(y=a \sec b x\).

\(y=\cos 4 x+2\)

Find the exact value of the expression. \(\sin \frac{23 \pi}{12}\)

\(g(x)=2 \tan x\)

\(y=-\cos 2 x\)

Find the exact value of the expression. \(\sin \left(-165^{\circ}\right)\)

\(g(x)=3 \tan x\)

\(y=\sin 3 \pi x\)

Find the exact value of the expression. \(\cos 105^{\circ}\)

\(g(x)=\cot 3 x\)

\(y=\cos \frac{\pi x}{4}\)

Find the exact value of the expression. \(\cos \frac{11 \pi}{12}\)

\(g(x)=\cot 2 x\)

\(y=\frac{1}{2} \cos 0.75 x-8\)

Find the exact value of the expression. \(\tan \frac{17 \pi}{12}\)

In Exercises 9-14, use the unit circle to evaluate the six trigonometric functions of \(\theta\). \(\theta=0^{\circ}\)

\(g(x)=3 \cot \frac{1}{4} x\)

\(y=3 \sin 0.2 x+6\)

Find the exact value of the expression. \(\sin \left(-\frac{7 \pi}{12}\right)\)

Use the unit circle to evaluate the six trigonometric functions of \(\theta\). \(\theta=540^{\circ}\)

\(g(x)=4 \cot \frac{1}{2} x\)

In Exercises 11-16, evaluate the expression given that \(\cos a=\frac{4}{5}\) with \(0

Use the unit circle to evaluate the six trigonometric functions of \(\theta\). \(\theta=\frac{\pi}{2}\)

\(g(x)=\frac{1}{2} \tan \pi x\)

MODELING WITH MATHEMATICS A middle-A tuning fork vibrates with a frequency \(f\) of 440 hertz (cycles per second). You strike a middle-A tuning fork with a force that produces a maximum pressure of 5 pascals. Write and graph a sine model that gives the pressure \(P\) as a function of the time \(t\) (in seconds).

Use the unit circle to evaluate the six trigonometric functions of \(\theta\). \(\theta=\frac{7 \pi}{2}\)

\(g(x)=\frac{1}{3} \tan 2 \pi x\)

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. \(g(x)=3 \sin x\)

\(\sin \theta=\frac{7}{11}\)

Evaluate the expression given that \(\cos a=\frac{4}{5}\) with \(0

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

ERROR ANALYSIS Describe and correct the error in finding the period of the function \(y=\cot 3 x\).

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. \(g(x)=2 \sin x\)

\(\cos \theta=\frac{5}{12}\)