A2t-personalperiodicproject
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Name ________________________________ Mr. Yates Algebra II with Trigonometry
Date __________
Period ______
Personal Periodic Functions Project
You each will receive two randomly-chosen periodic functions to investigate, of the form y = f(x) = a*sin(bx) + c*cos(dx). You will find and organize values of each function into a table, plot the points in a graph, and describe such properties of your function as domain, range, zeros, period, and amplitude. Then you will compare and contrast the properties of your two functions, research uses of periodic functions, and put your information together into a brief report.
Rubric (70pts total) 5: title page 2 - picture of each graph 3 – title, name, date 25: patterns and questions 15 – 5 each, questions 1-3 10 – research and examples (question 4) 40: details on your two specific functions (20 each) 1 – function named 3 - graph 3 - points in table 2 - domain 1 - range 1 – max 1 - min 2 - zeros 3 – amplitude 3 - period
Teacher’s Comments:
1 – function named 3 - graph 3 - points in table 2 - domain 1 - range 1 – max 1 - min 2 - zeros 3 – amplitude 3 - period
Questions to Answer: 1) Which function was more interesting to you, and why?
2) What properties were the same for both functions? List as many as you notice.
3) What different properties did the two functions have? Can any of these be explained by the coefficients (numbers) in your functions’ formulas?
4) Research periodic functions online and state two uses or real-world applications of periodic functions. For each application, explain (~3 sentences) how periodic functions are used in that context.
f(x) =
x -4π -7π/2 -3π -5π/2 -2π -7π/4 -3π/2 -5π/4 -π -5π/6 -3π/4 -2π/3 -π/2 -π/3 -π/4 -π/6 0 π/6 π/4 π/3 π/2 2π/3 3π/4 5π/6 π 5π/4 3π/2 7π/4 2π 5π/2 3π 7π/2 4π
f(x)
Domain (possible x):
Range (possible y):
Maximum:
Minimum:
Amplitude:
Period:
Zeros:
f(x) =
x -4π -7π/2 -3π -5π/2 -2π -7π/4 -3π/2 -5π/4 -π -5π/6 -3π/4 -2π/3 -π/2 -π/3 -π/4 -π/6 0 π/6 π/4 π/3 π/2 2π/3 3π/4 5π/6 π 5π/4 3π/2 7π/4 2π 5π/2 3π 7π/2 4π
f(x)
Domain (possible x):
Range (possible y):
Maximum:
Minimum:
Amplitude:
Period:
Zeros:
Date __________
Period ______
Personal Periodic Functions Project
You each will receive two randomly-chosen periodic functions to investigate, of the form y = f(x) = a*sin(bx) + c*cos(dx). You will find and organize values of each function into a table, plot the points in a graph, and describe such properties of your function as domain, range, zeros, period, and amplitude. Then you will compare and contrast the properties of your two functions, research uses of periodic functions, and put your information together into a brief report.
Rubric (70pts total) 5: title page 2 - picture of each graph 3 – title, name, date 25: patterns and questions 15 – 5 each, questions 1-3 10 – research and examples (question 4) 40: details on your two specific functions (20 each) 1 – function named 3 - graph 3 - points in table 2 - domain 1 - range 1 – max 1 - min 2 - zeros 3 – amplitude 3 - period
Teacher’s Comments:
1 – function named 3 - graph 3 - points in table 2 - domain 1 - range 1 – max 1 - min 2 - zeros 3 – amplitude 3 - period
Questions to Answer: 1) Which function was more interesting to you, and why?
2) What properties were the same for both functions? List as many as you notice.
3) What different properties did the two functions have? Can any of these be explained by the coefficients (numbers) in your functions’ formulas?
4) Research periodic functions online and state two uses or real-world applications of periodic functions. For each application, explain (~3 sentences) how periodic functions are used in that context.
f(x) =
x -4π -7π/2 -3π -5π/2 -2π -7π/4 -3π/2 -5π/4 -π -5π/6 -3π/4 -2π/3 -π/2 -π/3 -π/4 -π/6 0 π/6 π/4 π/3 π/2 2π/3 3π/4 5π/6 π 5π/4 3π/2 7π/4 2π 5π/2 3π 7π/2 4π
f(x)
Domain (possible x):
Range (possible y):
Maximum:
Minimum:
Amplitude:
Period:
Zeros:
f(x) =
x -4π -7π/2 -3π -5π/2 -2π -7π/4 -3π/2 -5π/4 -π -5π/6 -3π/4 -2π/3 -π/2 -π/3 -π/4 -π/6 0 π/6 π/4 π/3 π/2 2π/3 3π/4 5π/6 π 5π/4 3π/2 7π/4 2π 5π/2 3π 7π/2 4π
f(x)
Domain (possible x):
Range (possible y):
Maximum:
Minimum:
Amplitude:
Period:
Zeros:
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