January 26 th copyright2009merrydavidson 2 Example Determine the amplitude, period, and phase shift of y = 2sin (3x -  ) Solution: First factor out.

Slides:

Advertisements

Similar presentations

Graphing Trig Functions

Advertisements

February 8 th copyright2009merrydavidson Warm up: Factor These. 1)y 2 – 812) cos 2 x – 9 3)z 2 - 7z + 104) sin 2 x – 5sinx – 6 5) x 2 + 2x – 86) tan 2.

Graphs of the Sine, Cosine, & Tangent Functions Objectives: 1. Graph the sine, cosine, & tangent functions. 2. State all the values in the domain of a.

6.5 & 6.7 Notes Writing equations of trigonometric functions given the transformations.

4.5 Graphs of Sine and Cosine Functions

Notes Over 6.4 Graph Sine, Cosine Functions Notes Over 6.4 Graph Sine, Cosine, and Tangent Functions Equation of a Sine Function Amplitude Period Complete.

Problem of the Day. Section 4.5: Graphs of Sine and Cosine Functions. Pages What you should learn Sketch the graphs of basic sine and cosine.

Graphs of the Sine and Cosine Functions Section 4.5.

Copyright © 2009 Pearson Education, Inc. CHAPTER 6: The Trigonometric Functions 6.1The Trigonometric Functions of Acute Angles 6.2Applications of Right.

7-4 Evaluating and Graphing Sine and Cosine Objective: To use reference angles, calculators or tables, and special angles to find values of the sine and.

Trig – Section 4 Graphing Sine and Cosine Objectives: To graph sine and cosine curves To find amplitude, period and phase shifts.

Unit 5 – Graphs of the other Trigonometric Functions Tangent and Cotangent MM4A3. Students will investigate and use the graphs of the six trigonometric.

4.5 Graphs of Sine and Cosine y = sin x Fill in the following chart for sin x.

4.5 Sinusoidal Graphs Sketching and Writing Equations.

Objectives Graphs of Sine and Cosine

MAT 204 SP Graphs of the Sine and Cosine Functions 7.8 Phase shift; Sinusoidal Curve Fitting In these sections, we will study the following topics:

Quiz Find a positive and negative co-terminal angle with: co-terminal angle with: 2.Find a positive and negative co-terminal angle with: co-terminal.

Graphs Transformation of Sine and Cosine

Graphs of Sine and Cosine Five Point Method. 2 Plan for the Day Review Homework –4.5 P odd, all The effects of “b” and “c” together in.

The Coordinate Plane. A coordinate plane is formed when two number lines intersect. The coordinate plane is used to locate points. The two number lines.

Graphs of Trig Functions

Graphs of the Sine and Cosine Functions

MTH 112 Elementary Functions Chapter 5 The Trigonometric Functions Section 6 – Graphs of Transformed Sine and Cosine Functions.

Today you will use shifts and vertical stretches to graph and find the equations of sinusoidal functions. You will also learn the 5-point method for sketching.

MAT 204 FALL Graphs of the Sine and Cosine Functions 7.8 Phase shift; Sinusoidal Curve Fitting In these sections, we will study the following.

Graphs of the Sine and Cosine Functions Section 6.

January 24 th copyright2009merrydavidson. y = cos x.

Using Transformations to Graph the Sine and Cosine Curves The following examples will demonstrate a quick method for graphing transformations of.

Cofunction Identities

CHAPTER 4 – LESSON 1 How do you graph sine and cosine by unwrapping the unit circle?

Section 5.3 Trigonometric Graphs

Amplitude, Period, and Phase Shift

Graphs of Cosine Section 4-5.

14.1, 14.2 (PC 4.5 & 4.6): Graphing Trig Functions HW: p.912 (3-5 all) HW tomorrow: p.913 (6, 10, 16, 18), p.919 (12-16 even) Quiz 14.1, 14.2: Tuesday,

Starter Draw the graph of y = log(x+1) for -6≤ x ≤ 14. Draw in the asymptote Asymptote is at x = -1.

Section 6.6 Graphs of Transformed Sine and Cosine Functions Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

6.3 Graphing Sine and Cosine Functions. Periodic Functions A periodic function is a function with a repeating pattern this includes sin and cos graphs.

Do Now:. 4.5 and 4.6: Graphing Trig Functions Function table: When you first started graphing linear functions you may recall having used the following.

Section 3.5 Graphing Techniques: Transformations.

Translations of Sine and Cosine Functions

December 4, 2012 Using Translations on Sine and Cosine Curves Warm-up: 1. What is the domain for ? 2.Write the equation, then state the domain and range.

Periodic Function Review

5.2 Transformations of Sinusoidal Functions Electric power and the light waves it generates are sinusoidal waveforms. Math

Essential Question: What are the period and amplitude of the sine/cosine function? How do you find them? How do you graph sine and cos? Students will write.

GRAPHING SINE/COSINE FUNCTIONS Section 5.4. How to find the amplitude and period when given the graph of a function. 2.The period is the distance traveled.

Label each of the following graphs with the appropriate function. Calculator should be set to radians. Window Xscl should be set to pi. The amplitude equals:

Module 6.4 Graphing Sine and Cosine Functions with Different Amplitudes and Periods.

Sin & Cos Graphs Section 4.5.

2.7 Sinusoidal Graphs; Curve Fitting

6.5 – Translation of Sine and Cosine Functions

How do we recognize and graph periodic and trigonometric functions?

Chapter 4: Lesson 4.5 Graphs of Sine and Cosine Functions

Work on worksheet with 8 multiple choice questions.

Copyright © 2009 Pearson Education, Inc.

5.2 Transformations of Sinusoidal Functions

Amplitude, Period, and Phase Shift

Graphs of Sine and Cosine

6-5 Translating Sine and Cosine

Notes Over 6.4 Graph Sine, Cosine Functions.

Warm Up Write answers in reduced pi form.

State the period, phase shift, and vertical shift

Graphing Trigonometric Functions

Frequency and Phase Shifts

4.5 Basic Sine/Cosine Graphs

4.2 – Translations of the Graphs of the Sine and Cosine Functions

U8P2D6 Have out: Bellwork:

Warm Up Sketch one cycle of the sine curve:

Warm Up Sketch one cycle of the sine curve:

7.4 Periodic Graphs & Phase Shifts Objectives:

Presentation transcript:

January 26 th copyright2009merrydavidson

2 Example Determine the amplitude, period, and phase shift of y = 2sin (3x -  ) Solution: First factor out the 3 y = 2 sin 3(x -  /3) Amplitude = |A| = 2 period = 2  /B = 2  /3 phase shift = C/B =  /3 right

Section 4.5 1) Fill in the sine value for each given angle on the worksheet.

4.5 2) Put these values on the coordinate plane using the angle measures on the x axis and the sine value on the y axis. 0  will be at the origin.

3) Sketch in the curve. (not straight lines)

4) The curve oscillates between ____ and ____. What is the range of the sine curve? ______ 1 [-1, 1]

How to graph the sine curve. Start at the origin – or the MIDDLE go MIDDLE go HIGH go LOW go MIDDLE THE LEFT SIDE of the graph IS THE OPPOSITE.

5) Graph y = 2 sin  The amplitude is 2 The period because B is 1. How many sections on each side? Label them o o Put dots on the lines for middle, high, middle, low. H:y=2 L:y=-2 M:y=0 y-axis x-axis

6) Graph y = sin2  The amplitude is 1 The period because B is 2. How many sections on each side? Label them o o Put dots on the lines for middle, high, middle, low. y-axis x-axis H:y=1 M:y=0 L:y=-1

7)graph What do you know? A is 1/3, reflect over x-axis (go middle then LOW), B is pi/2, x means radians. What is the period? = 4 4 notches to the right and left H: y=1/3 L:y=-1/3 x-axis y-axis M:y=0

8) Graph y = sin  +2 The amplitude is 1; But the graph is shifted up 2. The period because B is 1. y-axis x-axis H:y=3 M:y=2 L:y= o o

9)graph What do you know?A is 1, B is 1, theta means 90 degrees right. What is the period? notches to the right and left. H:y=1 L:y= start at o o Draw in y-axis LAST. y = sin (  ) x-axis y-axis M:y=0

Write the equation for the given graph using the origin as the start point. What is the period? What is the amplitude? Find “B”. y = 2cos2x Is this sine or cosine? cosine

Fill in summary page on WS.

Quiz next class over: * Graph sine and cosine curves with transformations. *Answer questions about amplitude, period, phase shift and vertical shift. *Write the equation for a sine and/or cosine graph from given information. *Given a graph, find specific attributes.