1.
\(50^\circ\)
Answer.
\(\frac{5\pi}{18}\)
Exercises 5.7 Practice Problems
Answers to the odd-numbered excercises are included.
Exercise Group.
Change to radian measure:
2.
\(120^\circ\)
3.
\(375^\circ\)
Answer.
\(\frac{25\pi}{12}\)
4.
\(-12^\circ\)
Exercise Group.
Change to degree measure:
5.
\(-\frac{5\pi}{6}\)
Answer.
\(-150^\circ\)
6.
\(\frac{35\pi}{12}\)
7.
\(\frac{7\pi}{8}\)
Answer.
\(157.5^\circ\)
8.
\(-\frac{2\pi}{3}\)
Exercise Group.
Find the function values:
9.
\(\sin\frac{5\pi}{3}\)
Answer.
\(-\frac{\sqrt{3}}{2}\)
10.
\(\tan\frac{\pi}{6}\)
11.
\(\csc\frac{11\pi}{4}\)
Answer.
\(\sqrt{2}\)
12.
\(\cos\left(-\frac{2\pi}{3}\right)\)
13.
\(\sec\frac{11\pi}{6}\)
Answer.
\(\frac{2}{\sqrt{3}}\)
14.
\(\sin\left(-\frac{3\pi}{2}\right)\)
15.
\(\cot\frac{5\pi}{4}\)
Answer.
\(1\)
16.
\(\cos\frac{5\pi}{6}\)
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.
\(\cos\theta = -\frac{2\sqrt{2}}{3}\text{,}\) \(\tan\theta=-\frac{1}{2\sqrt{2}}\text{,}\) \(\sec\theta=-\frac{3}{2\sqrt{2}}\text{,}\) \(\cot\theta=-2\sqrt{2}\text{,}\) \(\csc\theta=3\text{.}\)
18.
\(\sec\theta=\frac{5}{3}\text{,}\) I
19.
\(\tan\theta=5\text{,}\) III
Answer.
\(\cos\theta=-\frac{1}{\sqrt{26}}\text{,}\) \(\sin\theta=-\frac{5}{\sqrt{26}}\text{,}\) \(\sec\theta=-\sqrt{26}\text{,}\) \(\csc\theta=-\frac{\sqrt{26}}{5}\text{,}\) \(\cot\theta=\frac{1}{5}\text{.}\)
20.
\(\cot\theta=-4\text{,}\) IV
21.
Find the six trigonometric function values for the following \(\theta\text{:}\)
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 \(8\text{.}\)
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:
22.
\(\tan x = \sqrt{3}\)
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 \(\left\{\frac{\pi}{4}+\frac{n}{2}\pi\right\}\text{.}\)
24.
\(2\sin^2x - 5\sin x + 2 = 0\)
Exercise Group.
Solve, finding all solutions in \([0,2\pi]\text{:}\)
25.
\(\sec^2 x - 4 = 0\)
Answer.
\(\left\{\frac{\pi}{3}, \frac{2\pi}{3}, \frac{4\pi}{3}, \frac{5\pi}{3} \right\}\)
26.
\(2\sin^3 x = \sin x\)
27.
\(\cos 2x \sin x + \sin x = 0\)
Answer.
\(\left\{0, \pi, 2\pi, \frac{\pi}{2}, \frac{3\pi}{2}\right\}\)
28.
\(\sec^2x = 4\tan^2 x\)
29.
\(\cos 2x - \sin x = 1\)
Answer.
\(\left\{0, \pi, 2\pi, \frac{7\pi}{6}, \frac{11\pi}{6}\right\}\)
