McKeague/Turner - Trigonometry 6e - Chap 4, Form D
Multiple Choice
____
1. Find all values of x for which the following is true.
a.
b.
c.
d.
e.
____
2. Find the algebraic expression that is equal to
.
a.
b.
c.
d.
e.
____
3. Find the algebraic expression that is equal to
.
a. 1
b.
c.
d.
e.
____
4. Find the algebraic expression that is equal to
.
a.
b.
c.
d.
e.
252
McKeague/Turner - Trigonometry 6e - Chap 4, Form D
____
5. The current in an alternating circuit varies in intensity with time. If I represents the intensity of the current and
t represents time, then the relationship between I and t is given by
where I is measured in
amperes and t is measured in seconds. Find the maximum value of I and the time it takes for I to go through
one complete cycle.
a. The maximum value of I is 20 amperes; one complete cycle takes
b. The maximum value of I is 160 amperes; one complete cycle takes
____
seconds.
seconds.
c. The maximum value of I is 40 amperes; one complete cycle takes
seconds.
d. The maximum value of I is 20 amperes; one complete cycle takes
seconds.
e. The maximum value of I is 40 amperes; one complete cycle takes
seconds.
6. A weight is hung from a spring and set in motion so that it moves up and down continuously. The velocity v
of the weight at any time t is given by the equation
where v is measured in meters per second
and t is measured in seconds. Find the maximum velocity of the weight and the amount of time it takes for the
weight to move from its lowest position to its highest position.
a. The maximum velocity is 5.5 meters per second ; the time it takes for the weight to move
from its lowest position to its highest position is
seconds.
b. The maximum velocity is 5.5 meters per second ; the time it takes for the weight to move
from its lowest position to its highest position is
seconds.
c. The maximum velocity is 22 meters per second ; the time it takes for the weight to move
from its lowest position to its highest position is
seconds.
d. The maximum velocity is 22 meters per second ; the time it takes for the weight to move
from its lowest position to its highest position is
seconds.
e. The maximum velocity is 4.5 meters per second ; the time it takes for the weight to move
from its lowest position to its highest position is
seconds.
253
McKeague/Turner - Trigonometry 6e - Chap 4, Form D
____
7. Sketch the graph of
from
to
by making a table using multiples of
a.
d.
b.
e.
c.
254
for .
McKeague/Turner - Trigonometry 6e - Chap 4, Form D
____
8. Use the graph of the equation
the equation
shown below to identify the graph of one complete cycle of
.
a.
d.
b.
e.
c.
255
McKeague/Turner - Trigonometry 6e - Chap 4, Form D
____
9. Identify the graph of the equation.
a.
d.
b.
e.
c.
256
McKeague/Turner - Trigonometry 6e - Chap 4, Form D
____ 10. For the given equation, first identify the phase shift and then sketch one complete cycle of the graph. Graph y
= sin x on the same coordinate system.
a.
d.
b.
e.
c.
257
McKeague/Turner - Trigonometry 6e - Chap 4, Form D
____ 11. For the given equation, first identify the phase shift and then sketch one complete cycle of the graph. Graph y
= cos x on the same coordinate system.
a.
d.
b.
e.
c.
258
McKeague/Turner - Trigonometry 6e - Chap 4, Form D
____ 12. Graph one complete cycle of
. Label the axes accurately.
a.
d.
b.
e.
c.
259
McKeague/Turner - Trigonometry 6e - Chap 4, Form D
____ 13. Graph one complete cycle of the graph. Label the axes accurately and identify the period.
a.
d.
b.
e.
c.
260
McKeague/Turner - Trigonometry 6e - Chap 4, Form D
____ 14. Find the equation of the line. Write your answer in slope-intercept form,
.
a.
b.
c.
d.
e.
____ 15. The graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find
an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is
correct.
a.
b.
c.
d.
e.
261
McKeague/Turner - Trigonometry 6e - Chap 4, Form D
____ 16. The graph below is one complete cycle of the graph of an equation containing a trigonometric function. Find
an equation to match the graph. If you are using a graphing calculator, graph your equation to verify that it is
correct.
a.
b.
c.
d.
e.
262
McKeague/Turner - Trigonometry 6e - Chap 4, Form D
____ 17. Sketch the graph from
to
.
a.
d.
b.
e.
c.
263
McKeague/Turner - Trigonometry 6e - Chap 4, Form D
____ 18. Sketch the graph from
to
.
a.
d.
b.
e.
c.
264
McKeague/Turner - Trigonometry 6e - Chap 4, Form D
____ 19. Sketch the graph from
to
.
a.
d.
b.
e.
c.
265
McKeague/Turner - Trigonometry 6e - Chap 4, Form D
____ 20. Sketch the graph from
to
.
a.
d.
b.
e.
c.
266
McKeague/Turner - Trigonometry 6e - Chap 4, Form D
____ 21. Use your graphing calculator to graph the function between
. (Make sure your calculator is set to radian mode.)
a.
d.
b.
e.
c.
267
and
. Show the graph of
,
, and
McKeague/Turner - Trigonometry 6e - Chap 4, Form D
____ 22. Use your graphing calculator to graph the function between
. (Make sure your calculator is set to radian mode.)
a.
d.
b.
e.
c.
268
and
. Show the graph of
,
, and
McKeague/Turner - Trigonometry 6e - Chap 4, Form D
____ 23. Graph
between
and
, and then reflect the graph about the line y = x to obtain the graph of
.
a.
d.
b.
e.
c.
269
McKeague/Turner - Trigonometry 6e - Chap 4, Form D
____ 24. Evaluate without using a calculator.
a.
b.
c.
d.
e.
____ 25. Simplify
if
.
a.
b.
c. x
d.
e.
270
McKeague/Turner - Trigonometry 6e - Chap 4, Form D
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
A
D
A
E
E
B
B
C
D
E
E
C
A
E
A
C
C
B
E
E
D
B
E
E
D
271