Math 5 Trigonometry
Chapter 4 Test
fall ’06 Name_________________________
Show your work for credit. Write all responses on separate paper.
1.
For arclength extending counterclockwise along the unit
circle from (1,0)
a. Find the reference number for t.
b. Find the coordinates of the terminal point P(x,y).
c.
Illustrate this point’s position on a plot of the unit
circle.
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2.
Suppose a.
Approximate to the nearest tenth the interval of x values corresponding to this t interval. b. Approximate to the nearest tenth the interval of y values corresponding to this t interval. |
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3.
In the diagram at right, P is the terminal point for a.
Explain why b.
What are the coordinates of Q in terms of x and y?
Use symmetry, but do not assume that you know the coordinate values. c.
Set up an equation in terms of d. Use the fact that (x,y) is on the |
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unit circle to substitute for y in terms of x and solve the resulting equation for x.
e. Substitute your value for x into the equation for in (c) and solve for y.
4.
The terminal point for an arc length t on the unit circle is .
Find sin t, cos t and tan t.
5.
Write tan t in terms of cos t, assuming the terminal point for t is in quadrant II.
6.
Find the amplitude, period and phase shift of and construct a careful, large graph showing
one period of the function.
7.
Find an equation for the sinusoid whose graph is shown:
8.
Consider the function .
a. Find the equations for two adjacent vertical asymptotes and sketch them in with dashed lines.
b. Find the x-coordinates of three points that divide the interval between the vertical asymptotes into 4 equal parts and evaluate the function at these three points.
c.
Construct a careful, large graph of the function
showing how it passes through the three points and how it approaches the
vertical asymptotes.
9. Suppose sin t = 3/5 and t is in the first quadrant. Find the following:
a.
b.
c.