Math 1316.S71 – Trigonometry
Professor Merrill
Name:_______________________________
Lab 2
Part I
Sketch two complete cycles of each graph. Draw and label axis. Label all critical points.
1. y  3sin 5
(degrees)
3
4
2. y  12 cos 
3. y  3sin

4
(degrees)
x (radians)
4. y  7 cos 2 x
(radians)
Amp: _______
Period: _______
EP: ________
CI: ________
D: ___________
Range: _____
Amp: _______
Period: _______
EP: ________
CI: ________
D: ___________
Range: _____
Amp: _______
Period: _______
EP: ________
CI: ________
D: ___________
Range: _____
Amp: _______
Period: _______
EP: ________
CI: ________
D: ___________
Range: _____
Equations for Sinusoidal Curves
Part II
Work with class.
Give the period, amplitude and an equation for the graphs shown.
1.
2.
Period: ________Amplitude: ______
Period:________Amplitude:_______
Equation: ________________________
Equation: _______________________
3.
Period: ______________Amplitude: _________
Equation: ______________________________
Work independently - Lab
Part III
Give the period, amplitude and an equation for the graphs shown. Be sure to check your answers by
graphing on the calculator.
4.
5.
Period: ______________
Period: _____________
Amplitude: ____________
Amplitude: ____________
Equation: ______________________
Equation: _________________________
6.
7.
Period: ______________
Period: _____________
Amplitude: ____________
Amplitude: ____________
Equation: _____________________
Equation: _________________________
Part IV
1. Describe the effects of A, B, C, and D for y  C  A sin B   D 
A: ____________________________________________________________
B: ____________________________________________________________
C: ____________________________________________________________
D: ____________________________________________________________
Do with Class
Sketch two complete cycles of each graph. Clearly label all critical points.

1. y  4  cos   30


2. y  6  sin  x 


(degrees)
 (radians)
2
Amp: _______
Period: _______
EP: ________
CI: ________
D: ___________
Range: _____
Amp: _______
Period: _______
EP: ________
CI: ________
D: ___________
Range: _____
Work Independently - Lab
Part V
Sketch two complete cycles of each graph. Label all critical points.

1. y  5  sin   50


2. y  7  cos   110


3. y  3  sin  x 


2
4. y  1  cos  x   
(degrees)

(degrees)
(radians)
(radians)
Amp: _______
Period: _______
EP: ________
CI: ________
D: ___________
Range: _____
Amp: _______
Period: _______
EP: ________
CI: ________
D: ___________
Range: _____
Amp: _______
Period: _______
EP: ________
CI: ________
D: ___________
Range: _____
Amp: _______
Period: _______
EP: ________
CI: ________
D: ___________
Range: _____
Writing Equations for Sinusoidal Curves
Part VI
Work with class.
Determine period, amplitude, horizontal and vertical shifts and equations for the graph shown.
1.
P:_______________ B:___________ A: ___________ VS:_______________ PS:_____________
Sin Equation:_______________________________________________________________________
Cos Equation:_______________________________________________________________________
2.
P:_______________ B:___________ A: ___________ VS:_______________ PS:_____________
Sin Equation:_______________________________________________________________________
Cos Equation:_______________________________________________________________________
Work independently - Lab
Part VII
Determine period, amplitude, horizontal and vertical shifts and two equations for the graph shown. Be
sure to check your answers by graphing on the calculator.
3.
P:_______________ B:___________ A: ___________ VS:_______________ PS:_____________
Sin Equation:_______________________________________________________________________
Cos Equation:_______________________________________________________________________
4.
P:_______________ B:___________ A: ___________ VS:_______________ PS:_____________
Sin Equation:_______________________________________________________________________
Cos Equation:_______________________________________________________________________
5.
P:_______________ B:___________ A: ___________ VS:_______________ PS:_____________
Sin Equation:_______________________________________________________________________
Cos Equation:_______________________________________________________________________
6.
P:_______________ B:___________ A: ___________ VS:_______________ PS:_____________
Sin Equation:_______________________________________________________________________
Cos Equation:_______________________________________________________________________
Tangent & Cotangent Graphs
Part VIII
Work With Class
Sketch two complete cycles of each graph.
1
4
1. y  tan 
Work Independently – Lab
Part IX
2. y  cot
4. y  tan

6
x
1
x
2
3. y  2  7 tan
1
  100
3
5. y  3  cot 2  x   

Harmonic Motion
Part X
Work With Class
1. A weight suspended from a spring is set into oscillating motion by compressing it to a point 3 cm above
its position and releasing it. It takes 1.2 seconds for the weight to complete one cycle.
Make a sketch of the curve.
Write an equation to describe the curve:_______________________
Determine the value of y when t = 2.2 s:____________________
Approximate the value of t when y = 2.5 for the first time:__________
Work Independently – Lab
Part XI
2. High tide in a bay is 2.6 meters above sea level and low tide is 2.6 meters below sea level. The time
between high tides is 12 ¼ hours. Assume that low tide occurs at t = 0 hours.
Make a sketch of the curve.
Write an equation to describe the curve:_______________________
Determine the value of y when t =20 hours:____________________
Approximate the value of t when y = 2 for the second time:_________
3. The horizontal distance “d” of the tip of a pendulum from its vertical position at rest can be
represented by a sinusoidal function. The tip of the pendulum has a maximum displacement of 7.5 inches
and completes one cycle in 3.1 sec. Assume that the pendulum is at rest at t = 0 and swings forward
first.
Make a sketch of the curve.
Write an equation to describe the curve:_______________________
Determine the value of y when t = 3.1 s:____________________
Approximate the value of t when y = 4 for the second time:_________
4. The usual 110-V household alternating current varies from –155 V to 155 V with a frequency of 60
cycles/ sec ( frequency is the reciprocal of period ). Assume the current starts at rest and then rises.
Make a sketch of the curve.
Write an equation to describe the curve:_______________________
Determine the value of y when t = 1/90 sec.:____________________
Approximate the value of t when y = 100 for the first time:________