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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,

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Presentation on theme: "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,"— Presentation transcript:

1 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

2 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

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

4 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

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

6 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

7 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.

8 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

9 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

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

11

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

13 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)

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

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

16 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    /2 3  /2 - 1  2 0 2    /2 1 5  /2 + 1  8.85

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

18 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 0 3  /2  2 1 2  +1   /2 0 5  /2  7.85

19 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, ODD, 42,45 EC) Problems not finished will be left as homework. Conclusion


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