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TRIGONOMETRY, 4.0: STUDENTS GRAPH FUNCTIONS OF THE FORM F(T)=ASIN(BT+C) OR F(T)=ACOS(BT+C) AND INTERPRET A, B, AND C IN TERMS OF AMPLITUDE, FREQUENCY, PERIOD, AND PHASE SHIFT. Graphing Sine and Cosine Functions

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Objectives Key words 1. Graph the equations of sine and cosine functions given the amplitude, period, phase shift, and vertical translation 2. Write equations given a graph. 3. Graph compound functions Midline Amplitude Maximum Minimum Period Sine curve Cosine curve Phase shift Graphing Sine and Cosine Functions

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Quick check! Can you find the distance between two numbers? Can you find the midpoint between two numbers?

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Order does matter! y=A sin[B(θ-h)]+k y=A cos[B(θ-h)]+k y=A sin[B(θ-h)]+k y=A cos[B(θ-h)]+k 1: Graphing Sine and Cosine Functions

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State the amplitude, period, phase shift, and vertical shift for y = 4cos(x / 2 + π) - 6. Then graph the function.

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1: Graphing Sine and Cosine Functions State the amplitude, period, phase shift, and vertical shift for y = 4cos(x / 2 + π) - 6. Then graph the function. Amplitude is 4 Period is 4π Phase shift is -2π Vertical shift is -6

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1: Graphing Sine and Cosine Functions State the amplitude, period, phase shift, and vertical shift for y = 2cos(x / 4 + π) - 1. Then graph the function.

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1: Graphing Sine and Cosine Functions State the amplitude, period, phase shift, and vertical shift for y = 2cos(x / 4 + π) - 1. Then graph the function. Amplitude is 2 Period is 8π Phase shift is -4π Vertical shift is -1

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Order does matter! y=A sin[B(θ-h)]+k y=A cos[B(θ-h)]+k y=A sin[B(θ-h)]+k y=A cos[B(θ-h)]+k 2: Write Equations of Sine and Cosine

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State the amplitude, period, phase shift, and vertical shift for the graph of: 2: Write Equations Example

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YOU TRY! State the amplitude, period, phase shift, and vertical shift for the graph of:

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2: Write Equations Example YOU TRY! State the amplitude, period, phase shift, and vertical shift for the graph of: Vertical shift is 0, midline y=0 Amplitude is 3 Period is 2 π/3 Phase shift is π/3 f(x) = 3cos(3x + π)

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Types of Compound Functions For Example: Compound functions may consist of sums or products of trigonometric functions or other functions. 3: Graph Compound Functions

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Graph y = x + sin x. 3: Graph Compound Functions

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Graph y = x + sin x. First create a table of each graph: y = x or y = sin x 3: Graph Compound Functions xsin xx + sin x 000 /2 1 /2 + 1 2.57 0 3.14 3 /2 3 /2 - 1 3.71 22 0 2 6.28 5 /2 1 5 /2 + 1 8.85

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YOU TRY: Graph y = x + cos x. First create a table of each graph: y = x or y = cos x 3: Graph Compound Functions

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YOU TRY: Graph y = x + cos x. First create a table of each graph: y = x or y = cos x 3: Graph Compound Functions xcos xx + cos x 011 /2 0 /2 1.57 -1 2.14 3 /2 0 3 /2 4.71 22 1 2 +1 7.28 5 /2 0 5 /2 7.85

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Summary Assignment Now you know how to graph sinusoidal functions Ask questions while you finish the assignment Finish missing work Exam Thursday/Friday 6.5 Translations of Sine and Cosine Functions pg383#(14-20 ALL, 21-37 ODD, 42,45 EC) Problems not finished will be left as homework. Conclusion

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Graphs of the Sine and Cosine Functions Section 6.

Graphs of the Sine and Cosine Functions Section 6.

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