Basic Technical Mathematics, 11th Edition

CHAPTER 10 REVIEW EXERCISES

CONCEPT CHECK EXERCISES

Determine each of the following as being either true or false. If it is false, explain why.

1. A point on the graph of $y\hspace{0.17em}=\hspace{0.17em}2\cos x$ is $(\pi \hspace{0.17em},\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}2)\hspace{0.17em}.\hspace{0.17em}$

2. The period of the graph of $y\hspace{0.17em}=\hspace{0.17em}4\sin {\displaystyle \frac{1}{2}}\pi x$ is 4.

3. The displacement of the graph of $y\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}2\cos (2x\hspace{0.17em}-\hspace{0.17em}{\displaystyle \frac{\pi }{4}})$ is $\hspace{0.17em}-\hspace{0.17em}{\displaystyle \frac{\pi }{8}}\hspace{0.17em}.\hspace{0.17em}$

4. The amplitude of the graph of $y\hspace{0.17em}=\hspace{0.17em}3\tan 2x$ is 3.

5. The frequency of an alternating current described by the equation $i\hspace{0.17em}=\hspace{0.17em}8\sin 60\pi t$ (t in s) is 120 Hz.

6. The graph of $y\hspace{0.17em}=\hspace{0.17em}\sin x\hspace{0.17em}-\hspace{0.17em}2\cos {\displaystyle \frac{1}{2}}x$ passes through $(\pi \hspace{0.17em},\hspace{0.17em}0)\hspace{0.17em}.\hspace{0.17em}$

PRACTICE AND APPLICATIONS

In Exercises 7–34, sketch the curves of the given trigonometric functions. Check each using a calculator.

7. $y\hspace{0.17em}=\hspace{0.17em}{\displaystyle \frac{2}{3}}\sin x$

8. $y\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}4\sin x$

9. $y\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}2\cos x$

10. $y\hspace{0.17em}=\hspace{0.17em}2.3\cos (\hspace{0.17em}-\hspace{0.17em}x)$

11. $y\hspace{0.17em}=\hspace{0.17em}2\sin 3x$

12. $y\hspace{0.17em}=\hspace{0.17em}4.5\sin 12x$