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Math 181
Dual Credit
Review Sheet – Revised Sp2014
This review is a collection of sample questions used by instructors of this course at
Missouri State University. It contains a sampling of problems representing the material
covered throughout the semester and may not contain every type of question on the final exam.
Please also be aware that a few questions on the final exam, while requiring knowledge and
understanding of the content covered in the course, may be presented in a form different than the
problems in the text.
1.
Find the angle that is complementary to  :
  32 4510
2.
Find the angle that is supplementary to  :
  125.9
3. Find the exact degree measure of the angle:
13
6
4. Find the exact radian measure of the angle: 315
5. Find the arc length of a circle with the given radius & central angle:   120 r  4 cm
6. Find the area of the sector of a circle with the given radius & central angle:   120 r  4 cm
7 Find the quadrant containing the point P on the unit circle U for the given conditions: sin t  0 and sec t  0
8 Use the fundamental identities to write the first expression in terms of the second, if 0  t   2
cos t , csc t
9. Use the fundamental identities to find the values of the trigonometric functions for the given conditions:
cos t 
12
and tan t  0
13
10. Verify the identity by transforming the left side into the right side.
sec   cos 

sin   tan 
11. Verify the identity by transforming the left side into the right side.
sin (t )  cot (t )  cos t
12. Complete the statement by referring to the graph of a trigonometric function:
 2
As t  

,
tan t  ___________
13. Refer to the graph of y  sin x to find the exact values of t in the interval [0, 4 ] that satisfy the equation.
sin t 
 2
2
14. Use the graph of a trigonometric function to sketch the graph of the equation without plotting points.
y  csc t  1
15. Convert from degrees to radians. (a)
(b)
16. Perform the indicated operation and simplify.
(a)
(b)
17. Give the definitions of the six trigonometric functions
(a) on the unit circle
(b) on a right triangle
18. List the three Pythagorean trigonometric identities.
(a)
(b)
19. Verify the trigonometric identity:
20. Verify the trigonometric identity:
(c)
21. A guy wire runs from the ground to a cell tower. The wire is attached to the cell tower 150 feet above the ground. The
angle formed between the wire and the ground is
.
(a) Find the length of the guy wire. Round your answer to one decimal place.
(b) How far from the base of the tower is the guy wire anchored to the ground?
Round your answer to one decimal place.
22. Find the exact values of the six trigonometric functions of
with the given constraints:
and
23. Fill in the table. Please show your work below the table.
function
amplitude period phase shift
24. Let
.
(a) Find the amplitude: ___________
(b) Find the period: ______________
(c) Find the phase shift: ___________
(d) Find the endpoints of a one-cycle interval.
Starting point: ________________ Ending point: ________________
25. Set up a table and algebraically verify the identity
26. Let
and
. Is it true that
and
have the same domain?
Explain your answer.
27 Find the general solutions of the equation
28. Find the general solutions of the equation
.
.
29. Explain why the equation is not an identity. Then find one value of the variable for which the equation is not true.
(a)
(b)
30. Find the exact value of each expression. Express each answer with a single denominator.
(a)
(b)
31. Solve each equation.
(a)
(b)
(c)
32. Let
Use the symbols discussed in class in your answers.
(a) Find the domain. Express your answer in set notation.
(b) Write the equation for the system of vertical asymptotes.
(c) Write the equation for the system of
.
(d) Sketch the graph.
33. Verify the identity:
34. Verify the identity:
35. Verify the identity
36. Find a nonzero vector that is perpendicular to the vector 7 2
37. Perform the operations:
a)
<-2, 3> + <1, 4>
b)  2, 3    1, 4 
38. Find the acute angle between vectors <-2, 3> and <1, 4>.