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

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

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

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

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

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

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.

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

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

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

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

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)

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

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

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

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

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

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