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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:
9.
10.
11.
Answer . 12.
\(\cos\left(-\frac{2\pi}{3}\right)\)
13.
14.
\(\sin\left(-\frac{3\pi}{2}\right)\)
15.
16.
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 \(8\text{.}\)
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:
22.
23.
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.
Answer .
\(\left\{\frac{\pi}{3}, \frac{2\pi}{3}, \frac{4\pi}{3}, \frac{5\pi}{3} \right\}\)
26.
27.
\(\cos 2x \sin x + \sin x = 0\)
Answer .
\(\left\{0, \pi, 2\pi, \frac{\pi}{2}, \frac{3\pi}{2}\right\}\)
28.
29.
Answer .
\(\left\{0, \pi, 2\pi, \frac{7\pi}{6}, \frac{11\pi}{6}\right\}\)