How do we recognize and graph periodic and trigonometric functions?

Slides:

Advertisements

Similar presentations

4.5 – Graphs of the other Trigonometric Functions Tangent and Cotangent.

Advertisements

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

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.

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

Objective Recognize and graph periodic and trigonometric sine and cosine functions.

Section Frequency of Sine and Cosine Graphs.

Graphs Transformation of Sine and Cosine

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

State the amplitude and period for each function

Trigonometric Functions

Graphs of the Sine and Cosine Functions Section 6.

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

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

Graphs of Other Trigonometric Functions

Further Transformations

Graphs of Sine and Cosine

Chapter 14 Day 8 Graphing Sin and Cos. A periodic function is a function whose output values repeat at regular intervals. Such a function is said to have.

Translations of Sine and Cosine Functions

PHASE SHIFTS AND VERTICAL SHIFTS I can identify the transformations made to the Sine and Cosine graph. 5.4 I can construct the Sine and Cosine.

Rational Functions Essential Questions

How do we recognize and graph periodic and trigonometric functions?

Notes Over 14.2 Translations of Trigonometric Graphs Translation of a Sine Function Amplitude Period.

Think about riding a bike and pumping the pedals at a constant rate of one revolution each second. How does the graph of the height of one of your feet.

Chapter 6 Section 6.4 Translations of the Graphs of Sine and Cosine Functions.

Warm Up 1. Is the sine graph even or odd? 2. Is the cosine graph even or odd? 3. Sine has what kind of symmetry? 4. Cosine has what kind of symmetry? What.

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:

Notes Over 14.1 Graph Sine, Cosine, and Tangent Functions.

Drawing Trigonometric Graphs.. The Basic Graphs. You should already be familiar with the following graphs: Y = SIN X.

Holt McDougal Algebra 2 Graphs of Sine and Cosine Holt Algebra 2Holt McDougal Algebra 2 How do we recognize and graph periodic and trigonometric functions?

y = | a | • f (x) by horizontal and vertical translations

2.7 Sinusoidal Graphs; Curve Fitting

Unit 5 – Quadratics Review Problems

Objective: Graphs of sine and cosine functions with translations.

The Natural Base, e Essential Questions

6.5 – Translation of Sine and Cosine Functions

Warm Up Evaluate Find the measure of the reference angle for each given angle that would be on the unit circle ° 5.

14.2 Translations and Reflections of Trigonometric Graphs

U9L5: Graphing Trigonometric Functions

Chapter 4: Lesson 4.5 Graphs of Sine and Cosine Functions

Work on worksheet with 8 multiple choice questions.

Transformations of sine and cosine

Writing Equations of Trigonometric Graphs

Transforming Graphs of Cosine Functions Mr

How do we recognize and graph trigonometric functions?

Graphing Trig Functions

Notes Over 6.4 Graph Sine, Cosine Functions.

Radical Functions Essential Questions

Frequency and Phase Shifts

4.5 Basic Sine/Cosine Graphs

How do we recognize and graph periodic and trigonometric functions?

How do we recognize and graph periodic and trigonometric functions?

Grade 12 Advanced Functions (MHF4U) Unit 4: Trigonometry 2 Trigonometric Graphs Transformation 2 Mr. Choi © 2017 E. Choi – MHF4U - All Rights Reserved.

Sinusoidal Functions.

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

2-6 Families of Functions

Rational Functions Essential Questions

Grade 12 Advanced Functions (MHF4U) Unit 4: Trigonometry 2 Trigonometric Graphs Transformation 2 Mr. Choi © 2017 E. Choi – MHF4U - All Rights Reserved.

Writing Trig Functions

Warm-up 1) write 3 positive and 3 negative solutions to the equation:

Graphs of Sine and Cosine: Sinusoids

Section 4.5 Graphs of Sine and Cosine Functions

Determining the Function Obtained from a Series of Transformations.

5.1 Graphing Sine and Cosine Functions

How do we draw angles in standard position?

Graphing: Sine and Cosine

Graphs of Sine and Cosine Sinusoids

8.3 – Model Periodic Behavior

7.4 Periodic Graphs & Phase Shifts Objectives:

Drawing Trigonometric Graphs.

Presentation transcript:

How do we recognize and graph periodic and trigonometric functions? Graphs of Sine and Cosine Essential Questions How do we recognize and graph periodic and trigonometric functions? Holt McDougal Algebra 2 Holt Algebra 2

Translations of Trigonometric Graphs Translation of a Sine Function Amplitude Period

Translations of Trigonometric Graphs Translation of a Sine Function Amplitude Period Moving a graph left or right is called a phase shift.

You can combine the transformations of trigonometric functions You can combine the transformations of trigonometric functions. Use the values of a, b, h, and k to identify the important features of a sine or cosine function. Amplitude Phase shift y = asinb(x – h) + k Vertical shift Period

Translations of Trigonometric Graphs Draw one cycle of the function’s graph. Amplitude Period Translation down 2

Translations of Trigonometric Graphs Draw one cycle of the function’s graph. Amplitude Period Translation up 3

Translations of Trigonometric Graphs Draw one cycle of the function’s graph. Amplitude Period Translation right p

Translations of Trigonometric Graphs Draw one cycle of the function’s graph. Amplitude Period Translation left p

Translations of Trigonometric Graphs Draw one cycle of the function’s graph. Amplitude Period Translation right p/2

Translations of Trigonometric Graphs Draw one cycle of the function’s graph. Amplitude Period Reflection over x-axis

Translations of Trigonometric Graphs Draw one cycle of the function’s graph. Amplitude Period Reflection over x-axis

Lesson 11.1 Practice B