Name ___________________________________________________
Trig Graphs Test Review
Date ________________ Period _______
Algebra 2
Mr. K
Trigonometry Graphs Review
Part I: Multiple Choice. Write the number of the best choice on the line provided.
_______ 1.
What is the equation for the accompanying graph?
(1) y  cos2x
(3) y  2cos x
1
1
(2) y  cos x
(4) y  cos x
2
2

_______ 2.
_______ 3.



What is the period of the graph whose equation is y  3cos2x ?
(1) 180°
(2) 2
(3) 3
(4) 360°
What is the range of the function y  5sinx ?
(1) 0° ≤ x ≤ 360°
(3) -1 ≤ y ≤ 1
(2) 0° ≤ y ≤ 360°
(4) -5 ≤ y ≤ 5

What is the equation for the accompanying graph?
(1) y  3sin3x
(2) y  3sin x
(3) y  sin3x
1
 (4) y  sin x
3


_______ 5. What is the amplitude of the graph of the equation y  3cos2x ?
(2) 2
(3) 3
(4) 180
 (1) 1
_______ 4.
_______ 6.
Which equation is represented by the diagram
 at right?
(1) y  cot x
(2) y  csc x
(3) y  sec x
 (4) y  tan x


_______ 7. For which value of θ is tan undefined?

(1) 0
(2)
2
(3) π
(4) It is never undefined.


Part II: Graphing. For each question in this section, make a table of values and graph the
equations. Answer any questions that follow.
8.
Graph the equation y  2sin x 1 in the interval 0° ≤ x ≤ 360°.
9.
Graph the equation y  cos2x in the interval 0 ≤ x ≤ 360.

1
10. Graph the equation y  sin 3x in the interval -180° ≤ x ≤ 180°.
2

11. Graph the equation y  tan x in the interval 0° ≤ x ≤ 360°.

Systems of Trig Graphs
12. a) On the 
same set of axes, graph the equations y  2sin2x and y 
3
cos x in the
4
interval 0° ≤ x ≤ 360°.
b) Use the graph from part a to determine how many values of x in the given interval
are solutions to the equation
.


1
13. a) On the same set of axes, graph the equations y  3sin3x and y  cos x in the
2
interval 0° ≤ x ≤ 360°.
b) Use the graph from part a to determine how many values of x in the given interval
are solutions to the equation
.


Inverse Trig Graphs
14. Graph y = arcsinx on the interval −180°≤ ≤180° (Remember to make 2 tables)
b. How could the interval be changed to make this graph a function?
15. Graph y = arccosx on the interval 0°≤ ≤360° (Remember to make 2 tables)
b. How could the interval be changed to make this graph a function?
Part III: For each equation, determine the amplitude, range, frequency, and period.


16. y  2sin5x
17. y 17cos x
19. y  4sin12x
20. y 


1
1
cos x
4
2
1
18. y  cos2x
2


2
21. y  4 sin x
3
Part IV: Each of the following equations is shifted from the original y  cos x equation. For
each equation, give the direction of the shift (left, right, up, or down), and how many units
the graph is shifted.


22. y  cos x  4
  )  3
23. y  cos(x
24. y  2cos(x  30)
25. y  cos5x  7

Part V: Evaluate each of the following expressions. Final answers should be left in simplest
radical form.

26.
27.
28.
29.
30.
31.
Part VI: Find the value of the principal inverse function. Round your answer to the nearest
degree, if necessary.
32. arccos(-1/2)
33.
34.
35.
36.
−
37.
−
−