CHAPTER 10 PRACTICE TEST

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

Determine the amplitude, period, and displacement of the function $y = - 3 \sin (4 π x - π / 3) .$ $y = - 3 \sin (4 π x - π / 3) .$

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

$y = 0.5 \cos \frac{π}{2} x$ $y = 0.5 \cos \frac{π}{2} x$
$y = 2 + 3 \sin x$ $y = 2 + 3 \sin x$
$y = 3 \sec x$ $y = 3 \sec x$
$y = 2 \sin (2 x - \frac{π}{3})$ $y = 2 \sin (2 x - \frac{π}{3})$
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 $y = A \cos (2 π / T) t .$ $y = A \cos (2 π / T) t .$ T is the period (in s) of the motion. If $A = 0.200 in .$ $A = 0.200 in .$ and $T = 0.100 s,$ $T = 0.100 s,$ sketch two cycles of y vs t.
Sketch the graph of $y = 2 \sin x + \cos 2 x$ $y = 2 \sin x + \cos 2 x$ by addition of ordinates.
Use a calculator to display the Lissajous figure for which $x = \sin π t$ $x = \sin π t$ and $y = 2 \cos 2 π t .$ $y = 2 \cos 2 π t .$
Sketch two cycles of the curve of a projection of the end of a radius on the y-axis. The radius is of length R and it is rotating counterclockwise about the origin at 2.00 rad/s. It starts at an angle of $π / 6$ $π / 6$ with the positive x-axis.
Find the function of the form $y = 2 \sin b x$ $y = 2 \sin b x$ if its graph passes through $(π / 3, 2)$ $(π / 3, 2)$ and b is the smallest possible positive value. Then graph the function.

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