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

Slides:

Advertisements

Similar presentations

Tangent and Cotangent Graphs

Advertisements

Expressing asinx + bcosx in the forms

Reading and Drawing Sine and Cosine Graphs

Next  Back Tangent and Cotangent Graphs Reading and Drawing Tangent and Cotangent Graphs Some slides in this presentation contain animation. Slides will.

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.

Amplitude, Period, & Phase Shift

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,

4.5 Sinusoidal Graphs Sketching and Writing Equations.

Translations of sine and cosine graphs The graph will be shifted to the right by c. The graph will be shifted up d. We already know what A and B are used.

Graphs Transformation of Sine and Cosine

Trigonometry Revision θ Hypotenuse Opposite Adjacent O SH A CH O TA.

Trigonometric Ratios of Any Angle © P. A. Hunt

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.

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.

Nat 5 Creation of BASIC Trig Graphs Graphs of the form y = a sin xo

Created by Mr. Lafferty Graphs of the form y = a sin x o Trigonometry Graphs National 5 Graphs of the form y = a sin bx o Solving.

Trigonometric Functions

Chapter 6 – Graphs and Inverses of the Trigonometric Functions

Mathematics Transformation on Trigonometric Functions Science and Mathematics Education Research Group Supported by UBC Teaching and Learning Enhancement.

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

This is the graph of y = sin xo

Solving Trigonometric Equations Involving Multiple Angles 6.3 JMerrill, 2009.

1 TF.03.3a - Transforming Sinusoidal Functions MCR3U - Santowski.

If is measured in radian Then: If is measured in radian Then: and: -

Practice for tomorrow’s test (solutions included).

10.2 Translate and Reflect Trigonometric Graphs

Page 309 – Amplitude, Period and Phase Shift Objective To find the amplitude, period and phase shift for a trigonometric function To write equations of.

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

EXAMPLE 4 Combine a translation and a reflection Graph y = –2 sin (x – ). 2 3 π 2 SOLUTION STEP 1Identify the amplitude, period, horizontal shift, and.

EXAMPLE 1 Graph a vertical translation Graph y = 2 sin 4x + 3.

14.1 Trig. Graphs.

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,

Trigonometric Graphs.

EXAMPLE 1 Graph a vertical translation Graph y = 2 sin 4x + 3. SOLUTION STEP 1 Identify the amplitude, period, horizontal shift, and vertical shift. Amplitude:

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

Section 4.5 Graphs of Sine and Cosine. Sine Curve Key Points:0 Value: π 2π2π π 2π2π 1.

Describe the vertical shift in the graph of y = -2sin3x + 4. A.) Up 2 B.) Down 2 C.) Up 4 D.) Down 4.

Chapter 2 Trigonometric Functions of Real Numbers Section 2.3 Trigonometric Graphs.

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

UNIT 6: GRAPHING TRIG AND LAWS Final Exam Review.

Graphs of the form y = a sin x o Nat 5 Graphs of the form y = a sin bx o Phase angle Solving Trig Equations Special trig relationships Trigonometric Functions.

Translations of Trigonometric Graphs LESSON 12–8.

Chapter 6 Section 6.3 Graphs of Sine and Cosine Functions.

1 Lecture 7 of 12 Inverse Trigonometric Functions.

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

Trigonometry Graphs Graphs of the form y = a sin xo

Amplitude, Period, & Phase Shift

2.7 Sinusoidal Graphs; Curve Fitting

How do we recognize and graph periodic and trigonometric functions?

14.2 Translations and Reflections of Trigonometric Graphs

U9L5: Graphing Trigonometric Functions

Amplitude, Period, and Phase Shift

TRIGONOMETRIC GRAPHS.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Translations of Trigonometric Graphs.

Amplitude, Period, & Phase Shift

6-5 Translating Sine and Cosine

Notes Over 6.4 Graph Sine, Cosine Functions.

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

Drawing Trigonometric Graphs.

7.4 Periodic Graphs & Phase Shifts Objectives:

Trigonometric Functions

Drawing Trigonometric Graphs.

Presentation transcript:

Drawing Trigonometric Graphs.

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

Y= COS X

Y = TAN X

Changing Trigonometric Graphs. You should know how the following graphs differ from the basic trigonometric graphs: Y= 2 SIN X The 2 in front of the sin x changes the “amplitude” of the graph.

Y = 5 COS X As expected the amplitude of the graph is now 5. Hence the graph has a maximum value of 5 and a minimum value of –5.

Y = SIN 2X By introducing the 2 in front of the X, the “period” of the graph now becomes 360 o  2 = 180 o.

Y= COS 6X The period of the graph has now become 360 o  6 = 60 o as expected.

Y= SIN X + 1 The plus 1 has the effect of “translating” the graph one square parallel to the y axis.

Y = COS X - 5 The cosine graph is translated 5 squares downwards parallel to the y axis.

Y= – SIN X The minus sign in front of the function “reflects” the whole graph in the X axis.

Y = – COS X As expected the cosine graph is reflected in the X axis.

Summary Of Effects. (1) Y= K COS X & Y = K SINX +k - k The amplitude of the function is “K”. (2) Y = COS KX & Y = SIN KX 360  K The period of the function is “360  k”.

(3) Y= COS X + K & Y = SIN X + K +k - k Translates the graph + K or – K parallel to the y axis. (4) Y = - COS X & Y = - SIN X. Y = - COS X Reflects the graph in the x axis.

Combining The Effects. We are now going to draw more complex trigonometric graphs like the one shown above, by considering what each part of the equation does to the graph of the equation.

Example 1. Draw the graph of : y = 4sin2x + 3 Solution. Draw the graph of : y = sin x y = 4 sin x 4 y = 4 sin 2x 180 o y = 4sin 2x

Example 2 Draw the graph y = 2 – 6 cos 5x Solution. Draw the graph of : y = cos x y= 6cos5x 72 o 6 y = - 6cos5x y = 2 – 6 cos 5x

Creating A Phase Shift. Shown below is the graph of y = sin x o Now compare it with the graph of y= sin( x - 60 o ) + 60 o The graph is translated 60 o to the right parallel to the x axis.

Shown below is the graph of y = cos x. Now compare it to the graph of y = cos ( x + 45 o ) -45 o The graph is translated 45 o to the left parallel to the x axis.

From the previous examples we can now see that the equation: y = cos ( x - k ) & y = sin ( x - k) translates the graph k o to the right parallel to the x axis. y = cos x y = cos (x-k) + k o From the previous examples we can now see that the equation: y = cos ( x + k ) & y = sin ( x + k) translates the graph k o to the left parallel to the x axis.