Skip to main content

Precalculus Review Materials

Exercises 5.7 Practice Problems

Answers to the odd-numbered excercises are included.

Exercise Group.

Change to radian measure:

Exercise Group.

Change to degree measure:

Exercise Group.

Find the function values:

Exercise Group.

A function value and a quadrant are specified. Find the other five function values.

17.

\(\sin\theta=\frac{1}{3}\text{,}\) II
Answer.
\(\cos\theta = -\frac{2\sqrt{2}}{3}\text{,}\) \(\tan\theta=-\frac{1}{2\sqrt{2}}\text{,}\) \(\sec\theta=-\frac{3}{2\sqrt{2}}\text{,}\) \(\cot\theta=-2\sqrt{2}\text{,}\) \(\csc\theta=3\text{.}\)

19.

\(\tan\theta=5\text{,}\) III
Answer.
\(\cos\theta=-\frac{1}{\sqrt{26}}\text{,}\) \(\sin\theta=-\frac{5}{\sqrt{26}}\text{,}\) \(\sec\theta=-\sqrt{26}\text{,}\) \(\csc\theta=-\frac{\sqrt{26}}{5}\text{,}\) \(\cot\theta=\frac{1}{5}\text{.}\)

21.

Find the six trigonometric function values for the following \(\theta\text{:}\)
described in detail following the image
A right triangle with one acute angle labled \(\theta\text{.}\) The hypotenuse has length \(17\) and the leg adjacent to the angle labled \(\theta\) has length \(8\text{.}\)
Figure 5.7.1.
Answer.
\(\cos\theta=\frac{8}{17}\text{,}\) \(\sin\theta=\frac{15}{17}\text{,}\) \(\tan\theta=\frac{15}{8}\text{,}\) \(\sec\theta=\frac{17}{8}\text{,}\) \(\csc\theta=\frac{17}{15}\text{,}\) \(\cot\theta=\frac{8}{15}\text{.}\)

Exercise Group.

Solve, finding all solutions:

23.

\(2\cos^2 x = 1\)
Answer.
\(\left\{\frac{\pi}{4}+2n\pi, \frac{3\pi}{4}+2n\pi,\frac{5\pi}{4}+2n\pi, \frac{7\pi}{4}+2n\pi\right\}\) or \(\left\{\frac{\pi}{4}+\frac{n}{2}\pi\right\}\text{.}\)

Exercise Group.

Solve, finding all solutions in \([0,2\pi]\text{:}\)