6.5 & 6.7 Notes Determining the transformations to trigonometric functions.

Slides:

Advertisements

Similar presentations

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

Advertisements

We need to sketch the graph of y = 3sin(5t+90)

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

 Trigonometric of any Angle Pg. 501 – 514  LEARNING OBJECTIVES; Use the definitions of trigonometric functions of any angle.  Use the signs of the trigonometric.

Objectives Graphs of Sine and Cosine

C HAPTER 7: T RIGONOMETRIC G RAPHS 7.4: P ERIODIC G RAPHS AND P HASE S HIFTS Essential Question: What translation is related to a phase shift in a trigonometric.

2.6 – Vertical and Horizontal Translations

Section 4.6 Graphs of Other Trigonometric Functions.

6.4 Notes Graphing trigonometric functions transformationally: changes to coefficient A.

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.

The Sine Graph: Introduction and Transformations 26 April 2011.

Graphing Sinusoidal Functions y=sin x. Recall from the unit circle that: –Using the special triangles and quadrantal angles, we can complete a table.

Notes Over 14.5 Writing Trigonometric Functions Write a function for the sinusoid. Positive Sine graph No vertical or horizontal shifts Amplitude: Period:

The Trig Graphs Build-A-Graph Day (5.5). POD #1 Complete these limit statements. For limit statements, go to the graphs, not the unit circle. For which.

2.4 Use Absolute Value Functions and Transformations

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

Sinusoidal Curve Fitting

Amplitude, Period, and Phase Shift

5.8 Graphing Absolute Value Functions

14.1 Trig. Graphs.

Section 4.5 Graphs of Sine and Cosine. Overview In this section we first graph y = sin x and y = cos x. Then we graph transformations of sin x and cos.

6.5 Notes Graphing trigonometric functions transformationally: changes to C and D.

2.6: Absolute Value and Families of Functions. Absolute Value Ex1) Graph y = |x|

6.4 Notes Graphing trigonometric functions transformationally: changes to coefficient B.

6.6 DAY 2: More Elimination. 1. Line terms up vertically 2. Make sure one of the variables has opposite coefficients (Today, it is by multiplying…Like.

Simple Trigonometric Equations The sine graph below illustrates that there are many solutions to the trigonometric equation sin x = 0.5.

Warm up Find the amplitude, vertical shift, phase shift, and period.

EQ: How can transformations effect the graph a parent function? I will describe how transformations effect the graph of a parent function.

Graphing Trig Functions Review Whiteboard Activity.

Transformations of Linear and Absolute Value Functions

2.7 – Use of Absolute Value Functions and Transformations.

Vocabulary The distance to 0 on the number line. Absolute value 1.9Graph Absolute Value Functions Transformations of the parent function f (x) = |x|.

Vocabulary The function f(x) = |x| is an absolute value function. The highest of lowest point on the graph of an absolute value function is called the.

5.8 Graphing Absolute Value Functions I can graph an absolute value function and translate the graph of an absolute value function.

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.

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.

Graphing Trigonometric Functions Objective: To graph various trigonometric functions. VERTICAL DISPLACEMENT The graph of y = A sin(k  + c) + h is the.

Warm up If the graph above is y = sinx. Write a functions of each graph.

Graphing Tangent Section 4.6. Objectives Students will be able to… Use the unit circle to generate the parent graph of tangent Recognize the tangent parent.

Section 3.5 Trigonometric Functions Section 3.5 Trigonometric Functions.

6.7 Graphing Other Trigonometric Functions Objective: Graph tangent, cotangent, secant, and cosecant functions. Write equations of trigonometric functions.

Graphing y = tan x x = 0, tan (0) = _____ (, ) x = π/4, tan (π/4) = _____ (, ) x = π/2, tan (π/2) = _____ (, ) x = -π/4, tan (-π/4) = _____ (, ) x = -π/2,

Graphing Trigonometric Functions

Any questions from your homework? Be prepared to start notes right away.

5.6 Phase Shift; Sinusoidal Curve Fitting

Graphing Trigonometric Functions

Absolute Value Transformations

2 Understanding Variables and Solving Equations.

Solving 1-step Inequalities

Transformations: Review Transformations

How do we recognize and graph periodic and trigonometric functions?

Graphing Trigonometry Functions

Objective Graph and transform |Absolute-Value | functions.

Writing Equations of Trigonometric Graphs

Rev Graph Review Parent Functions that we Graph Linear:

Graphing Trigonometric Functions

Amplitude, Period, and Phase Shift

Translations of Trigonometric Graphs.

Periodic Function Repeats a pattern at regular intervals

Graphing Trigonometric Functions

Sinusoidal Functions.

Geometry 2 Level 1.

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

Predicting Changes in Graphs

What is your best guess as to how the given function

Graphic Organizer for Transformations

7.4 Periodic Graphs & Phase Shifts Objectives:

Presentation transcript:

6.5 & 6.7 Notes Determining the transformations to trigonometric functions

6.5 & 6.7 Notes Find the amplitude, period, phase shift, and vertical shift of the trigonometric function.

6.5 & 6.7 Notes The amplitude of a trigonometric function is the absolute value of the coefficient of trigonometric function. amplitude:

6.5 & 6.7 Notes The period of a trigonometric function is found by dividing the parent graph’s period by the coefficient of the angle variable, θ.

6.5 & 6.7 Notes The phase shift is in the direction indicated by the opposite sign of C in an amount equal to the value of C. It may be necessary to factor to find C.

6.5 & 6.7 Notes The vertical shift is in the direction indicated by the sign of D in an amount equal to the value of D.

6.5 & 6.7 Notes Find the amplitude, period, phase shift, and vertical shift of the trigonometric function.

6.5 & 6.7 Notes Find the amplitude, period, phase shift, and vertical shift of the trigonometric function.

6.5 & 6.7 Notes Find the amplitude, period, phase shift, and vertical shift of the trigonometric function.

6.5 & 6.7 Notes Find the amplitude, period, phase shift, and vertical shift of the trigonometric function.