trigonometric functions and graphsholyspiritmath3200.weebly.com/uploads/3/8/6/9/... · lesson 5.1...
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Lesson 5.1 Graphing sine and cosine function
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(i) Graph sine, cosine and tangent function
Characteristics:« domain and range« amplitude« period« zeros
(ii) Transformations of the sine and cosine function
(iii) Solve first and second degree trigonometric equations algebraically and graphically.
CHAPTER 5
Trigonometric Functions and Graphs
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Lesson 5.1 Graphing sine and cosine function
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Special Angles on the Unit Circle
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Lesson 5.1 Graphing sine and cosine function
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Summary:
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Lesson 5.1 Graphing sine and cosine function
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Lesson 5.1 Sketch the graph of and .
Choose 5 key points associated with each graph
determine the characteristics of the graph
A. Graph the function
The sine function
ycoordinate of the point
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Lesson 5.1 Graphing sine and cosine function
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Characteristics:
periodic function: a function that repeats itself over regular intervals (cycles) of its domain.
(i) period: the portion of the graph which illustrates one full cycle of the function.
one cycle:
sinusoidal function: a periodic function that looks like waves; oscillates repeatedly up and down from a centre line
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Lesson 5.1 Graphing sine and cosine function
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(ii) Maximum/Minimum
(iii) Domain/Range:
(iv) Horizontal Central Axis : the horizontal line which is halfway between the local maximum and local minimum.
Characteristics cont'd:
Equation of the Sinusoidal Axis
Midline
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Lesson 5.1 Graphing sine and cosine function
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Characteristics cont'd:
(v) Amplitude: vertical distance from the sinusoidal axis to a local maximum or minimum
(vi) x and yintercepts
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Lesson 5.1 Graphing sine and cosine function
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Choose 5 key points associated with each graph
determine the characteristics of the graph
B. Graph the function
The cosine function
the xcoordinate of the point
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Lesson 5.1 Graphing sine and cosine function
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(i) Maximum/Minimum:
(ii) Domain/Range:
(iv) Amplitude:
(iii) Horizontal Central Axis: (Equation of the Sinusoidal Axis)
(v) x and yintercepts
Characteristics:
one cycle:
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Lesson 5.1 Graphing sine and cosine function
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Compare the graph of to .
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Lesson 5.1 Graphing sine and cosine function
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Transformations: Vertical and Horizontal Stretches
Example1
Identify the amplitude for each function.
Vertical Stretch
(i)
affects the ______________
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Lesson 5.1 Graphing sine and cosine function
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Example 1 cont'd
(ii)
(iii)
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Lesson 5.1 Graphing sine and cosine function
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Horizontal Stretch
Example 2
Identify the horizontal stretch and the period for each function.
period: period:
b= b=
Solve an inequality to determine the length of the cycle and the key points (max,min,xints, hits SA)
affects the ______________
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Lesson 5.1 Graphing sine and cosine function
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Example 3 Graph the functions What is the period of ?
Solve an inequality
period:
b=
period:
b=
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Lesson 5.1 Graphing sine and cosine function
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What is the period of ?
Solve an inequality
Example 4: Graph the functions
period:
b=period:
b=
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Example 6: What is the period of ?
Example 5: What is the period of ?
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Lesson 5.1 Graphing sine and cosine function
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Example 7
Sketch the graph of for at least one cycle.
Determine • the amplitude • period • maximum and minimum values• x and yintercepts • domain and range.
Method 1: Use Mapping Rule
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Method 2: Use Inequality and Key Points
P.233236 #45 (no graph), 610, 14