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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
Lesson 5.1 Graphing sine and cosine function
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Special Angles on the Unit Circle
Lesson 5.1 Graphing sine and cosine function
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Summary:
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
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
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
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
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
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:
Lesson 5.1 Graphing sine and cosine function
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Compare the graph of to .
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 ______________
Lesson 5.1 Graphing sine and cosine function
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Example 1 cont'd
(ii)
(iii)
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 ______________
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=
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=
Lesson 5.1 Graphing sine and cosine function
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Example 6: What is the period of ?
Example 5: What is the period of ?
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
Lesson 5.1 Graphing sine and cosine function
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Method 2: Use Inequality and Key Points
P.233236 #45 (no graph), 610, 14