xUnit #7 Day #1 Periodic Functions Notes.notebook
November 22, 2016
Unit #7
Day #1
Periodic
Functions
Objectives:
Students will...
1. Determine if a function is periodic and identify a cycle, the period and the amplitude of the function.
2. Analyze angles in the coordinate plane and determine measures of co­terminal angles. 1
xUnit #7 Day #1 Periodic Functions Notes.notebook
November 22, 2016
Investigation: Suppose you and a friend are sitting on a Ferris wheel. When you first get on at the bottom of the ride, you are 5 feet above the ground on the platform. At the very top of the ride, you are 40 feet above where you started. Once the ride begins, the wheel moves at a constant speed. It takes 36 seconds to complete one revolution. 1a. At 0 seconds, when the ride starts, how high above the ground are you?
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xUnit #7 Day #1 Periodic Functions Notes.notebook
November 22, 2016
1b. What is your height at
9 seconds?
18 seconds?
27 seconds?
45 seconds?
1c. What is your height at 126 seconds?
How many revolutions have you made?
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xUnit #7 Day #1 Periodic Functions Notes.notebook
November 22, 2016
2. Sketch a graph showing the relationship between your height above the ground and the time since the ride began. Let the x­axis be time and the y­axis be the height.
This function you just graphed is called periodic. Using your graph, create a definition for a periodic function. 4
xUnit #7 Day #1 Periodic Functions Notes.notebook
November 22, 2016
Periodic Function ­ function with a repeating pattern of y­values at regular intervals.
Cycle ­ one complete pattern
Period ­ time to complete one cycle
horizontal length of one cycle
Amplitude ­ half the difference between the max and min value. the line halfway between the max and min value is known as the midline.
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xUnit #7 Day #1 Periodic Functions Notes.notebook
November 22, 2016
Which of the following functions is periodic?
Identify a cycle two different ways. Determine the period and amplitude.
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xUnit #7 Day #1 Periodic Functions Notes.notebook
November 22, 2016
Identify a cycle two different ways. Determine the period and amplitude.
Angles in the Coordinate Plane:
Angle ­ a rotation of a ray around its endpoint.
Angles in Standard Position:
The vertex of the angle (endpoint) is the origin.
The ray on the positive x­axis is called the initial side.
The other ray is called the terminal side.
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xUnit #7 Day #1 Periodic Functions Notes.notebook
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November 22, 2016
y
5
4
3
2
1
x
­6
­5
­4
­3
­2
­1
0
­1
1
2
3
4
5
6
­2
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­6
Find the measure of the angle in standard position.
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xUnit #7 Day #1 Periodic Functions Notes.notebook
November 22, 2016
Two Ways to Measure Angles:
Positive ­ move in a counterclockwise direction
Negative ­ move in clockwise direction
Draw the following angles in standard position. 9
xUnit #7 Day #1 Periodic Functions Notes.notebook
November 22, 2016
Coterminal Angles ­ angles in standard position with the same terminal side
Find one positive and one negative coterminal angle for each of the following.
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xUnit #7 Day #1 Periodic Functions Notes.notebook
November 22, 2016
Find the LEAST POSITIVE co­terminal angle for each of the following.
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