Math Analysis Ch. 5 – 6 Review
Highlight the topics below as you feel comfortable with each topic. Use your notes, practice
worksheets, and homework to study! Use your TRIG BOOK to help you with formulas. I’ve included
a few extra practice problems too. MOST problems are no calculator on the test. Keep that in mind as
you study!
Chapter 5
o 5.1 – 5.3 Trig Review
o Unit circle
o Reference angles
o Quadrants (all students take calculus)
o Finding theta given a problem like sin = ****
o 5.4 Graphing sine, cosine, tangent
o Graph at least two cycles and label all axes
o Period and amplitude
o Domain and range
o 5.5 Graphing cosecant, secant, cotangent
o Domain and range
o Asymptotes
o 5.6 Phase Shift
o y = a sin (bx – c) + d
Know how a, b, c, and d change the graph.
Chapter 6
o 6.1 – 6.2 Inverse trig
o Domain and range for inverse functions – note the restrictions
o True and false statements based on domain and range of inverse functions
o Solving inverses
o 6.3 Trig Proofs
o Pythagorean identities like cos2 + sin2 = 1
o Helpful tricks: factoring, multiplying by conjugates, common denominator
o 6.4 – 6.5 Angle Formulas – MEMORIZE!
o Sum and difference formulas for sin, cos, tan
o Double and half angle formulas for sin, cos, tan
o 6.7 – 6.8 Trig Equations
Find the exact value for each expression below.
1. cos-1 0
2. tan1 ( 3)

3

4. csc sin 1

2



 12 
5. tancos 1   
 13 

3. cot 1 ( 1)
 3 
6. cos 1 tan 
4

4 

7. cos 1  cos

3 

  
8. cos  
 12 
9. tan

8
Verify the following identity.
cos(   )
 cot   tan 
10.
cos  sin 
Find the exact value of each expression.
5
4

11. sin  cos 1  cos 1 
13
5

12 

12. cos 2 tan 1 
5

3
4

12
when     and cot  
when    
, find the exact values for…
2
3
2
5
13. tan(   )
 
 
14. sin  
15. cos 
2
2
Given tan   
Solve each equation on the interval [0, 2π).
16. sec2 θ = 4
17. sin(3θ) = 1
18. 8 – 12 sin2 θ = 4 cos2 θ
19. cos(2θ) = sin θ
Use a calculator to solve on the interval [0, 2π). Round to the nearest hundredth.
20. cos θ = 0.6
21. cot θ = 2
Find the reference angle for the given angle θ in standard position. (Find θ′.)
22. 295°
23. -490°
10
5
24.
25.
3
8
θ′ = _________
θ′ = _________
θ′ = _________
θ′ = _________
Find the exact value of each expression. KNOW THE UNIT CIRCLE!!!!!!
26. cos 150°
27. sin 225°
28. tan (-30°)
29. csc(90°)
30. sec(270°)
32. sin

3
33. cos 52
34. cot 116
35. sec( 73 )
36. csc(5 )
31. cot 45°
37. tan 72
Find values for θ where…
38. 0° < θ < 360° to the nearest tenth of a degree
39. 0 < θ < 2π to the nearest hundredth of a radian
sin θ = -0.3568
cot θ = 1.2479
θ = ___________________
θ = ___________________
In which quadrant does the terminal side of θ lie from standard position?
40. tan θ > 0 and csc θ < 0
41. sec θ < 0 and π < θ < 2π
42. cot   3
5
5
and sin  
70
14
Given the following information, find the exact value of the six trig functions.
43. (5, 9) is a point on the terminal side of θ.
44. The terminal side of θ intersects the unit circle at
Note: x = 5 and y = 9 (NOT cos = 5 and sin = 9)
 2 5 5

 . Note: since this is ON the unit
,


5
5


circle, the x and y values are the cos and sin values.
sin θ = ______ cos θ = ______ tan θ = ______
csc θ = ______ sec θ = ______ cot θ = ______
sin θ = ______ cos θ = ______ tan θ = ______
7 2
and cos θ > 0
2
csc θ = ______ sec θ = ______ cot θ = ______
19
46.  
6
sin θ = ______ cos θ = ______ tan θ = ______
sin θ = ______ cos θ = ______ tan θ = ______
csc θ = ______ sec θ = ______ cot θ = ______
csc θ = ______ sec θ = ______ cot θ = ______
45. csc  
Graph at least two cycles of the following functions.
48. g ( x )  3 csc( 2x )
47. f ( x )  tan 14 x
Period:_______
Period:_______
Domain:____________________________
Domain:____________________________
Range: _____________________________
Range: _____________________________