Lesson 6.4 Extra Practice
STUDENT BOOK PAGES 337–346
Copyright © 2009 by Nelson Education Ltd.
1. For each of the following trigonometric functions,
determine the period, amplitude, horizontal
translation, and equation of the axis.
␲x
a) y ⫽ 18 cos a b ⫺ 14
4
3␲
4
2
b) y ⫽ ⫺ sin a ax ⫹
bb ⫹ 10
5
7
4
9
7␲
c) y ⫽ 101 cos ax ⫺
b ⫺
4
10
d) y ⫽ 6 sin (␲x ⫹ 13) ⫹ 22
5␲
e) y ⫽ ⫺ cos a (x ⫺ 1)b ⫹ 1
3
x
f) y ⫽ 15 sin a b ⫺ 5
15
2. The function y ⫽ cos x is the parent function of each
of the following trigonometric functions, none of
which has undergone any horizontal translations or
reflections in either axis. Determine the equation of
each trigonometric function.
a) This trigonometric function has a period of 3, an
amplitude of 4, and an equation of the axis of
y ⫽ 5.
b) This trigonometric function has a period of 10␲,
an amplitude of 10␲ , and an equation of the axis
of y ⫽ 10␲ .
c) y ⫽ 99 sin (⫺9(x ⫹ 99)) ⫹ 9
3
d) y ⫽ sin (x ⫺ 6) ⫺ 2
4
4. Sketch the graphs of each of the following
trigonometric functions.
x
a) y ⫽ 5 cos a b ⫺ 4
3
1
␲
b) y ⫽ ⫺ sin ax ⫹ b
4
2
␲
c) y ⫽ 10 cos a2ax ⫺ bb ⫹ 8
4
3
d) y ⫽ sin (␲(x ⫹ 1))
2
5. Determine the equation of each of the following
trigonometric functions.
a)
y
2
–p
2
x
0
–p
4 –2
–4
–6
b)
p
4
p
2
y
1
x
3␲
c) This trigonometric function has a period of 8 , an
amplitude of 3, and an equation of the axis of
y ⫽ 8.
d) This trigonometric function has a period of 207 , an
amplitude of 207, and an equation of the axis of
y ⫽ ⫺7.
3. The function y ⫽ sin x is the parent function of each
of the following trigonometric functions. State the
transformations that have been applied to each.
1
1
a) y ⫽ ⫺ sin a (x ⫺ 3)b ⫹ 4
12
12
␲x
b) y ⫽ 14 sin a b ⫺ 7
14
–8p –4p
0
c)
4p
8p
p
2
p
y
x
–p
–p
2
0
–20
–40
Lesson 6.4 Extra Practice
473