Name ___________________________________________________
Test 11 Review
Date ________________ Period _______
Ms. Williams
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  2cosx
1
1
(2) y  cosx
(4) y  cos x
2
2


of the graph whose equation is y  3cos2x ?
_______ 2.  What is the period
(1) 180°
(2) 2
(3) 3
(4) 360°
_______ 3.
_______ 4.
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

Which function has the same period as y  4cos2x ?
(1) y  4cosx
(2) y  4sin x
(3) y  tan x
(4) y  tan2x
_______ 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


_______ 6. What is the amplitude of the graph of the equation y  3cos2x ?
(2) 2
(3) 3
(4) 180
 (1) 1
_______ 7.
_______ 8.
What is the minimum value in the range ofy  2sin x  3?
(1) 1
(2) 0
(3) -1
For which value of θ is tan undefined?


(1) 0
(2)
(3) π
2


(4) -5
(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.
9.
Graph the equation y  2sin x 1 in the interval - ≤ x ≤ .
Show work here!

10. Graph the equation y  cos 2 x in the interval 0 ≤ x ≤ 2π.
Show work here!
1
11. a) On the same set of axes, graph the equations y  sin x and y  3cosx in the
2
interval 0 ≤ x ≤ 2π
b) Use the graph from part a to determine how many 
values of x in the given interval

1
are solutions to the equation sin x  3cosx
2
Show work here!

1
12. a) On the same set of axes, graph the equations y  tan x and y  cosx in the
2
interval -2π ≤ x ≤ 2π
b) Use the graph from part a to determine how many values of x in the given interval

1
are solutions to the equation tan x  cos 2 x
2
Show work here!
Part III: For each equation, determine the amplitude, range, frequency, and period.
13. y  2 sin 5 x 
2
15. y  4 sin x
3
14. y 17cosx


Part IV: Identifying equations of trig graphs.
Write an equation for each graph.
16.
17.
18.
19.
Part IV:
Part V: Writing equations of phase shifts.