3.1 INTRODUCTION TO PERIODICFUNCTIONS:
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I) REVIEW: BASIC TRIGONOMETRY:
OppositeSide
Hypotenuse
AdjacentSide
Hypotenuse
SineFunction
CosineFunction
AdjacentSide
Oppositeside
TangentFunction
When solving for the angle, use the inverse trig. function
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EX: FIND THE MISSING SIDES TO 2 DECIMAL PLACES
Cross Multiply!
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PRACTICE: FIND THE MISSING ANGLE TO THENEAREST DEGREE
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II) WHAT IS A PERIODIC FUNCTION?
A function that repeats its output values in a cycle
The range of input values within a cycle is known as theperiod
There are many examples of periodic functions in ourworld
Ocean waves and ocean currents
Solar system
Finance and Market trends
Sound waves, light transmission, radiation
Wave propagation: earthquakes,
Heart beat
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III) COMPONENTS OF A PERIODIC FUNCTION:
x
y
Crest
Trough
Period
Crest: Local maximums on the periodic function. Top
Trough: Local minimums on the periodic function. Bottom
Amplitude: The vertical difference between the top and the middle
Period: The horizontal difference between two rests or two troughs
Note: The horizontal distance between the crest and trough is HALF the
period.
Amplitude
Period
½ of Period
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Ex: Given each graph, indicate the period and amplitude
x
y
-3
-2
-1
0
1
2
-4
-3
-2
-1
1
2
3
4
x
y
-3
-2
-1
0
1
2
-4
-3
-2
-1
1
2
3
4
Period
Amplitude
Period
Amplitude
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Ex: If high tide occurred at 7:30am and low tide was at1:30pm, what time will the next high tide be?
The time difference between high tide and low tide is half the period
The time for a full period will be 12 hours
So the next high tide will be 12 hours from 7:30am
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HIGH AND LOW TIDE:
At high tide, the ocean levels go up
At low tide, the ocean levels go down
Ocean levels will fluctuate
up and down over several hours
Ex: Indicate whether if the following graphs are periodicfunctions. If they are, state the period of the function:
x
y
-5
-4
-3
-2
-1
0
1
2
3
4
5
-3
-2
-1
1
2
3
x
y
-16
-12
-8
-4
0
4
8
12
16
1
2
3
Period
Period = 3units
Period
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