Download HW TGIE 1 Answers

TGIE-1
GRAPHING TRIGONOMETRIC FUNCTIONS
(PWL 4.5 – 4.6 AND AM 8-2 – 8-3)
HOMEWORK #1
I.
Complete the table below.
Amplitude
Reflected?
(Yes or No)
Period
2/B
3
no
Pi/2
Pi/8
Intercept
2.5
No
2/3
1/6
Max
1
4
Period
Max, Min, or
Intercept?
1)
y = 3 sin 4x
2)
y = 2.5 cos 3x
3)
y = -7 cos 2x
7
Yes
Pi
Pi/4
Min
4)
y = - sin x
1
Yes
2
1/2
Intercept
5)
y = 8 cos
x
8
No
4pi
pi
Max
6)
y = -2 sin
x
2
Yes
8
2
Intercept
II.
1
2
p
4
Graph two complete cycles of each of the following functions. Label all key
values and keep scale. Identify the domain and range of the function.
p
1)
y = 3 cos 2x
2)
y = 2 sin
3)
y = -4 sin 3x
4)
y = -2 cos x
MPH/CR 11/11
2
x
Precalculus
TGIE-1
GRAPHING TRIGONOMETRIC FUNCTIONS
(PWL 4.5 – 4.6 AND AM 8-2 – 8-3)
HOMEWORK #2
I.
Complete the table below.
Amplitude
Reflected?
(Yes or No)
Period
2/B
4
Yes
12pi
3pi
None
2) y = 7 sin 5x + 4
7
No
2pi/5
Pi/10
3) y = -3 sin 2 (x – 1)
3
Yes
1
1
No
11
5
1) y = -4 cos
4) y = cos
2
3
5) y = 11 sin
x
6
-1
x+3
4
9
x-6
6) y = 5 cos (x + 3) + 8
MPH/CR 11/11
Axis of
Wave
Max, Min, or
Intercept?
Down 1
y = -1
Min
none
Up 4
y = 4
Intercept
1/4
Right 1
None
y = 0
Intercept
3pi
3pi/4
None
Up 3
y = 3
Max
No
9pi/2
9pi/8
None
Down 6
y =-6
Intercept
No
2pi
Pi/2
Left 3
Up 8
y = 8
Max
1
4
Period
Horizontal
Shift
Vertical
Shift
2
Precalculus
II.
Graph two complete cycles of each of the following functions. Label all key values and keep scale. Identify
the domain and range of the function.
1)
y = 5 sin 2x + 3
3)
y = 2 cos
MPH/CR 11/11
2p
5
x-1
1
2)
y = 2 cos
4)
y = - 3 sin
2
x-2
p
4
x+1
3
Precalculus
TGIE-1
GRAPHING TRIGONOMETRIC FUNCTIONS
(PWL 4.5 – 4.6 AND AM 8-2 – 8-3)
HOMEWORK #3
I.
Complete the table below.
Amplitude
(
1) y - 3 = 2sin 4x - 8p
æ
ç
è
Period
2/B
1
4
Period
)
NO
Pi/2
Pi/8
p ö÷
÷
2ø
æp
ö
÷
x
p
ç
÷
2
è
ø
MPH/CR 11/11
Vertical
Shift
Axis of
Wave
Max, Min,
or
Intercept
Up 3
y=3
intercept
Up 2
y=2
Min
Down 5
y=-5
intercept
Up 8
y=8
Max
Left pi/2
3
YES
Pi/2
Pi/8
Right 2
3) y + 5 = 6sin ç
æ 2p
ö
ç
÷
4) y = 5cos
ç x - 4p ÷ + 8
è 3
ø
Horizontal
Shift
Right 2pi
2
2) y - 2 = -3cos 4 ç x +
Reflected
(Yes / No)
6
NO
4
1
Right 6
5
NO
3
¾
4
Precalculus
II.
Graph two complete cycles of each of the following functions. Label all key values and keep scale. Identify
the domain and range of the function. (AM page 313 #9-14)
1)
y = 3 + 5 sin2x
3)
y = 4 - 4cos2 x - p
5)
Y + 3 = 6sin
(
MPH/CR 11/11
p
4
)
2)
1
y = -2 + 2cos x
2
4)
y - 3 = 2cos
p
2
(x - 1)
(x + 2)
5
Precalculus
TGIE-1
GRAPHING TRIGONOMETRIC FUNCTIONS
(PWL 4.5 – 4.6 AND AM 8-2 – 8-3)
HOMEWORK #4
I.
Complete the table below.
Reflected?
(Yes or No)
1)
y = tan 6x
No
p
2)
y = -2tan
3)
æ
2ö
y = tan3p ççx - ÷÷ + 4
4
3ø
è
4)
æp
ö
ç
y = - tan ç x - 4p ÷÷ + 8
è2
ø
II.
3
x
1
Period
/B
1
2
Period
p
p
6
12
3
3
Yes
No
Yes
2
1
1
3
6
2
1
Horizontal
Shift
None
None
Right 2/3
Right 8
Vertical
Shift
None
None
Up 4
Up 8
Asymptotes
x=
np
12
n Î odd integer
x=
3n
2
n Î odd integer
x=
n
6
n Î odd integer
x =n
n Î odd integer
Graph two complete cycles of each of the following functions. Label all key values and keep scale. Identify
the domain, range and asymptotes of the function.
1) y = 4tanx
MPH/CR 11/11
2) y = - tan
(
2
p
)
x -3
3)
y = tan 4x – 2
4)
y = tan
1
2
(x + 2p ) - 1
6
Precalculus
MPH/CR 11/11
7