Algebra 2 STUDY GUIDE AIIT.18 Graphing Trig Functions
Mrs. Grieser
Name: _______________________________________ Date: ________________ Block: __________
Graphing Trig Functions TEST STUDY GUIDE
Test covers:

Know domain, range, period, and intercepts of the six parent trig functions.

Find amplitude, period, phase shift, and vertical displacement, as applicable, for all
six trig functions. Graph the functions applying transformations using this
information.

Writing equations of trig functions from a verbal description of amplitude, period,
phase shift, and/or vertical displacement, or from a given graph.
Practice Questions:
1) Graph each function, finding the requested information.
a) y = sin x
b) y = cos x
Domain_________
x-ints _________
Domain_________
x-ints _________
Range _________
y- int _________
Range _________
y- int _________
Period _________
Period _________
c) y = tan x
d) y = cot x
Domain_________
x-ints _________
Domain_________
x-ints _________
Range _________
y- int _________
Range _________
y- int _________
Period _________
Period _________
Algebra 2 STUDY GUIDE AIIT.18 Graphing Trig Functions
e) y = csc x
f)
Mrs. Grieser Page 2
y = sec x
Domain_________
x-ints _________
Domain_________
x-ints _________
Range _________
y- int _________
Range _________
y- int _________
Period _________
Period _________
2) For each trig function below, identify the applicable values: amplitude, period, phase
shift, vertical displacement, and whether graph is reflected.
a) y = sin 6x
b) y = - 5cos x
 
 
c) y = - sin 2 x     2
3 
 
d) y = 3cos3x     2


e) y = - 2sin x    5
6

f)
y = csc
g) y = cos

2

3
x
x
h) y = 1  4sec

10
x
i)
 
y = - 1  3cot2 x - 
 6
j)
y = 2  5tan

8
x  3
Algebra 2 STUDY GUIDE AIIT.18 Graphing Trig Functions
Mrs. Grieser Page 3
3) Graph the trig functions, finding the applicable values first: amplitude, period, phase
shift, vertical displacement, and whether graph is reflected.
a)
 x
y  4 cos 
3
amplitude: _______
b) y  4 sin 2 x 
amplitude: _______
period: ______
period: ______
c)
 x
y  csc 
3
amplitude: _______
d) y  cot 2 x 
amplitude: _______
period: _______
period: ______
e)


y  sin x  
4

amplitude: _______
period: _______
f)


y  tan x  
2

amplitude:
_______
period: _______
Algebra 2 STUDY GUIDE AIIT.18 Graphing Trig Functions
g) y  2 sin3x   2
amplitude: _______
period: ______
h) y 
Mrs. Grieser Page 4
1


cos x    2
2
4

amplitude: _______
period: ______
4) Given the graph, find the amplitude and period, then write a trig function.
a)
b)
5) Write an equation of a cosine function with amplitude 3, a period of π, a phase shift of
to the left, and translated 1 unit up.
6) Write an equation of a sine graph with a phase shift right 3, a period of 5π, a vertical
translation down 6, and an amplitude of 3.

4
Algebra 2 STUDY GUIDE AIIT.18 Graphing Trig Functions
Mrs. Grieser Page 5
STUDY GUIDE ANSWERS
1) a) D=(-∞, +∞);
R=[-1, 1];
period: 2π; xints: nπ ; y-int:
0
b) D=(-∞, +∞); R=[-1,
1]; period: 2π; x-ints:
c) D=all R except
d) D=all R except n ; R=(-∞, +∞); period: π; x-

2
n
; y-int: 1
2
 n ; R=(-∞, +∞);
ints:

2
 n ; y-
period: π; x-ints:
n ; y-int: 0
int: none
e) D=all R
except n ;
R=(-∞, -1]U[1,
∞); period: 2π;
x-ints:none; yint: none
f) D=all R except
2)
a) amp.:1; period:

2
1]U[1, ∞); period:
2π; x-ints:none;
y-int: 1

3
c) amp:1; period π; phase shift:
up 2; reflected
e)amp: 2; period: 2π; phase shift:
down 5; reflected
g) amp: 1; period: 6
 n ; R=(-∞, -
b) amp.:5; period: 2; reflected

left; translate
3

right; translate
6
d)amp: 3; period:
2

; phase shift:
left;
3
3
translate down 2
f) amp: n/a; period: 4


i) amp: n/a; period: ; phase shift:
right;
2
6
h) amp: n/a; period 40; translate up 1
j) amp: n/a; period 8; phase shift: 3 right;
translate up 2
translate down 1
3) a)
b)
Algebra 2 STUDY GUIDE AIIT.18 Graphing Trig Functions
Mrs. Grieser Page 6
c)
d)
e)
f)
g)
h)
4) a) amp: 4; period: 2π; y=4cos x
b) amp:5; period 2π; y = -5cos x
5) y = 3cos2 x 
6) y  sin
2
x  3  6
5





  1 or y = 3cos 2x    1
4
2
