Int. Trig.
Name: _____________________________
Weekend Practice - Analyzing Trig Functions
Amplitude
Trig Function
(Distance from
Midline)
sin or cos
Omega, ω
Date: ____________________ Pd: ______
X or ϴ
C
Vertical Shift
(VARIABLE)
C= -(PS)(ω)
(MIDLINE)
Y=
ω=
2
Pd
Write the equation of the trigonometric function with the given characteristics.
1. Sine Function; Amplitude=5; Vertical Reflection; Period=π; Phase Shift is LEFT 3 units; Midline at y=0
2. Cosine Function; Amplitude=3; Period=4π; Phase Shift is RIGHT π units; Midline at y=4
3. Cosine Function; Minimum value = -3; Maximum value = 3; Period=3π; Vertical Shift down 5; No Phase Shift
4. Sine Function; Minimum value = -5; Maximum value = 1; Period=π; Phase Shift is LEFT 4π
5. Secant Function; Amplitude is 0.5; Period=
2
2
; Vertical Shift Up 2 units; Phase Shift Right
3
3
6. Cosecant Function; Local Minimum is 7; Local Maximum 3; Period is π; No Phase Shift
7. Tangent Function; Amplitude is 5; Period=  ; Vertical Shift Up 9 units; No Phase Shift.
8. Cotangent Function; Phase shift left

4
; Peroid = 2 ; vertical shift down 3
Int. Trig.
Name: _____________________________
Weekend Practice - Analyzing Trig Functions
Amplitude
Trig Function
(Distance from
Midline)
sin or cos
Omega, ω
Date: ____________________ Pd: ______
X or ϴ
C
Vertical Shift
(VARIABLE)
C= -(PS)(ω)
(MIDLINE)
Y=
ω=
2
Pd
Write the equation of the trigonometric function with the given characteristics.
1. Sine Function; Amplitude=5; Vertical Reflection; Period=π; Phase Shift is LEFT 3 units; Midline at y=0
2. Cosine Function; Amplitude=3; Period=4π; Phase Shift is RIGHT π units; Midline at y=4
3. Cosine Function; Minimum value = -3; Maximum value = 3; Period=3π; Vertical Shift down 5; No Phase Shift
4. Sine Function; Minimum value = -5; Maximum value = 1; Period=π; Phase Shift is LEFT 4π
5. Secant Function; Amplitude is 0.5; Period=
2
2
; Vertical Shift Up 2 units; Phase Shift Right
3
3
6. Cosecant Function; Local Minimum is 7; Local Maximum 3; Period is π; No Phase Shift
7. Tangent Function; Amplitude is 5; Period=  ; Vertical Shift Up 9 units; No Phase Shift.
8. Cotangent Function; Phase shift left

4
; Peroid = 2 ; vertical shift down 3
Analyze Real-World Sinusoidal Functions. Read the given statements and answer the questions that follow.
 
m   10
6 
9. The amount of daylight (hrs) in Quito, Ecuador can be represented by the equation d  2 cos 
(where m=1 represents January 1st, m=2 represents February 1st, etc.)
a. What is the maximum amount of daylight in Quito?
b. What is the minimum amount of daylight in Quito?
c. When does the maximum amount of daylight occur?
(Find Month)
d. When does the minimum daylight occur?
(Find Month)
e. Graph what is going on here.
10. A ferris wheel with center 50 feet above the ground has a maximum height of 90 feet. It takes 5 minutes for the
ferris wheel to make a full rotation
a. Draw a picture of what is happening.
b. How far off the ground must the riders be to get on the ride (Min)?
c. How long does it take for the riders to reach the maximum?
d. Write an equation for the situation.
e. What is the height of a rider after 3 min 45 sec?
f.
How long does it take a rider to reach a height of 50 feet?
Analyze Real-World Sinusoidal Functions. Read the given statements and answer the questions that follow.
9.
 
m   10
6 
The amount of daylight (hrs) in Quito, Ecuador can be represented by the equation d  2 cos 
(where m=1 represents January 1st, m=2 represents February 1st, etc.)
a. What is the maximum amount of daylight in Quito?
b. What is the minimum amount of daylight in Quito?
c. When does the maximum amount of daylight occur?
(Find Month)
d. When does the minimum daylight occur?
(Find Month)
e. Graph what is going on here.
10. A ferris wheel with center 50 feet above the ground has a maximum height of 90 feet. It takes 5 minutes for the
ferris wheel to make a full rotation
a. Draw a picture of what is happening.
b. How far off the ground must the riders be to get on the ride (Min)?
c. How long does it take for the riders to reach the maximum?
d. Write an equation for the situation.
e. What is the height of a rider after 3 min 45 sec?
f.
How long does it take a rider to reach a height of 50 feet?