Study Guide for PART II of the Fall 2015 MAT187 Final Exam. Wednesday December 16th 7:00 a.m. – 8:50 a.m.
NO CALCULATORS are permitted on this part of the Final Exam. This part of the Final exam will consist of 50 multiple
choice questions. You will be provided with one sheet of scratch paper which must be turned in with your exam
regardless of whether or not you use the scratch paper. You may NOT use your own scratch paper.
This portion of the exam covers the Trigonometry portion of this course (4.1 – 4.12). You should focus on your notes
and homework from those sections and Tests #5 and #6. Of course some of you may benefit from utilizing the
supplemental reading and videos on the class Help page from these sections too!
Here is a brief overview of what you should be able to do!
1. Be able to convert a degree measure into a radian measure (where
 will be part of your answer). Try 2550

2. Be able to evaluate a trig function at a particular degree measure. Example: cos 1200
3. Be able to utilize you unit circle to find the value of trig expressions like cos

4

 sin
3
2
4. Know which trig functions are positive and which ones are negative in each quadrant!
5. Given a standard angle on the unit circle, be able to identify the coordinates.

6. Be able to find the value of an inverse trig function expression. Example: arctan  


3
 . Be sure to practice arcos
3 
and arcsin problems from your notes and homework too.






7. Be able to find the value of composed trig functions and inverse trig functions. Example: sin  arccos  
Find others in your notes and homework to practice!
8. Be able to evaluate various trig functions at certain degree measures. Example:
cos300 ,  cos 2100 ,sin 600 ,  sin 600
9. Be able to calculate the length of an arc when given the radius and angle (in radians). See section 4.4
10. Can you solve tan x  cot x ? Think about the unit circle!
11. Be able to simplify a basic trigonometric expression. Example:
cot 
csc 
12. Can you simplify 1  sin x 1  sin x  ?
13. What is sin 600 cos 400  cos 600 sin 400 equivalent to? cos1000 ,sin1000 ,cos 200 ,sin 200 .
3 
 .
2  
14. If sin A 
3
5
and
cos B 
5
13
what does cos  A  B   ? What about sin  A  B  ?
15. Be able to simplify trigonometric expressions involving double angles. (go look some up!)
16. Be able to solve basic trig equations in restricted domains. Example: Solve tan x  3  0 in
1800 ,3600 
17. Given a modified Sine equation be able to figure out the amplitude.
18. Given a modified Sine equation be able to figure out the period.
19. Given a modified Sine equation be able to figure out the horizontal shift.
20. Given the graph of a modified Sine function be able to select the corresponding equation.
21. Given a modified Sine equation be able to pick out the correct graph.
22. Make sure that you know the domains of Sine, Cosine and Tangent.
23. Given two sides of a triangle and the included angle, be able to estimate the area.
24. Given two angles and one side of an angle, be able to find one of the remaining sides.
25. If cos 2 A  
24
. What is the value of sin A ? Make sure that YOU know all three versions of identity #21!
25
26. Be able to use the Law of Sines to solve problems like. In triangle ABC,
B  600
c  8 and
sin C 
1
4
Find the length of side b
27. Be able to solve a SSS triangle for the largest angle. Since you are not allowed a calculator then obviously the side
lengths must be chosen in such a way to yield an angle that you can obtain WITHOUT the use of a calculator!
28. Be able to solve a SAS triangle for the missing side. You should be able to estimate the answer without a calculator
given your knowledge of the few basic decimals I told you to know.
29. Be able to find an exact value for a trig expression involving lesser used trig functions. Example:
csc 600  cot 300  csc 450
30. Be able to compute compositions of regular trig functions with inverse trig functions. Like #7 BUT different trig and
inverse trig functions AND you will need to draw a triangle rather than use the unit circle!
31. Given an angle in standard position and the coordinates of a point on the terminal side be able to obtain the value
of any trig function for that angle.
32. Can you find the exact value of sin 3150  tan1350 ?
33. If cos  
3
4
and  is in quadrant IV, find the value of sin2 .
34. Given a modified cosine equation, be able to find the period.
35. What is cos7 x cos3x  sin 7 x sin3x equivalent to? Be sure you know the sum and difference identities for both
sine and cosine.
36. Be able to simplify a trig expression involving cos 2
37. Make sure that you know identity #9 and the several other versions of it that we have used in this course.
38. Make sure that you understand the relationship between a trigonometric function and its inverse.
39. Be able to find a reference angle for a given degree measure.


40. Can you find an angle x in the third quadrant where cot x  300  tan x ? What about in the other quadrants?
41. Can you find an angle coterminal to another angle?
42. Be sure to know for what values sin,sin 1 ,cos,cos1 , tan
and
tan 1 are defined. i.e. What are the domains of
each?
43. Be able to find a solution to a trig equation involving sine and cosine.
44. Can you find cot 1 1 ? sec1  2  ?
45. Be able to solve a very basic sine or cosine equation in the interval  00 ,3600
46. Can you simplify basic expressions like

cot x
?
cos x
47. Be sure that you know the “word” definitions for each of the six regular trig functions. i.e. sin  
48. Be sure that you know the range of each of arcsin x, arc cos x
and
opposite
hypotenuse
arctan x
49. Know when you should use each of the following to find the missing side of a triangle.. Pythagorean theorem, Law
of Sines, Law of Cosines, Similar triangles.
50. Be able to calculate the area of a triangle when you are given two sides and the included angle.