Basic Technical Mathematics, 11th Edition

CHAPTER 10 PRACTICE TEST

As a study aid, we have included complete solutions for each Chapter Test problem at the back of this book.

1. Determine the amplitude, period, and displacement of the function $y\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}3\sin (4\pi x\hspace{0.17em}-\hspace{0.17em}\pi \hspace{0.17em}/\hspace{0.17em}3)\hspace{0.17em}.\hspace{0.17em}$

In Problems 2–5, sketch the graphs of the given functions.

2. $y\hspace{0.17em}=\hspace{0.17em}0.5\cos {\displaystyle \frac{\pi }{2}}x$

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

4. $y\hspace{0.17em}=\hspace{0.17em}3\sec x$

5. $y\hspace{0.17em}=\hspace{0.17em}2\sin (2x\hspace{0.17em}-\hspace{0.17em}{\displaystyle \frac{\pi }{3}})$

6. A wave is traveling in a string. The displacement y (in in.) as a function of the time t (in s) from its equilibrium position is given by $y\hspace{0.17em}=\hspace{0.17em}A\cos (2\pi \hspace{0.17em}/\hspace{0.17em}T)t\hspace{0.17em}.\hspace{0.17em}$ T is the period (in s) of the motion. If $A\hspace{0.17em}=\hspace{0.17em}0.200\text{ in}\hspace{0.17em}.\hspace{0.17em}$ and $T\hspace{0.17em}=\hspace{0.17em}0.100\text{ s}\hspace{0.17em},\hspace{0.17em}$ sketch two cycles of y vs t.

7. Sketch the graph of $y\hspace{0.17em}=\hspace{0.17em}2\sin x\hspace{0.17em}+\hspace{0.17em}\cos 2x$ by addition of ordinates.

8. Use a calculator to display the Lissajous figure for which $x\hspace{0.17em}=\hspace{0.17em}$