Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1 Inverse, Exponential, and Logarithmic Functions Copyright © 2013, 2009, 2005 Pearson Education,

Slides:



Advertisements
Similar presentations
Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1 5 Trigonometric Identities.
Advertisements

7 TECHNIQUES OF INTEGRATION. 7.2 Trigonometric Integrals TECHNIQUES OF INTEGRATION In this section, we will learn: How to use trigonometric identities.
Section 6.1 Rational Expressions.
8.4 Relationships Among the Functions
Pre-calc w-up 1/16 2. Simplify cos 2 x tan 2 x + cos 2 x Answers: / cos50 o 3. 1.
Warm up  If, find.  Express cos 490o as a trig function of an angle in Quadrant 1.  Simplify.
Section 5.1 Verifying Trigonometric Identities. Overview In Chapter 4, we developed several classes of trigonometric identities: 1.Quotient 2.Reciprocal.
Verifying Trigonometric Identities
1 8.3 Trigonometric Identities In this section, we will study the following topics: o Using trig identities and algebra to simplify trigonometric expressions.
Verifying Trigonometric Identities Section 5.2 Math 1113 Created & Presented by Laura Ralston.
6.3 – Trig Identities.
Pre calculus Problems of the Day Simplify the following:
Verifying Trigonometric Identities T,3.2: Students prove other trigonometric identities and simplify others by using the identity cos 2 (x) + sin 2 (x)
Trigonometric Identities I
What you will learn How to use the basic trigonometric identities to verify other (more complex) identities How to find numerical values of trigonometric.
Copyright © Cengage Learning. All rights reserved. 7 Techniques of Integration.
Verifying Trigonometric Identities. Remember that a conditional equation is true for only some values in the domain. So you solve the equation by finding.
Chapter 5.2.
Copyright © Cengage Learning. All rights reserved. CHAPTER The Six Trigonometric Functions The Six Trigonometric Functions 1.
Barnett/Ziegler/Byleen College Algebra with Trigonometry, 6 th Edition Chapter Seven Trigonometric Identities & Conditional Equations Copyright © 1999.
Chapter 11: Trigonometric Identities
Section 5.1 Verifying Trigonometric Identities.
Copyright © 2000 by the McGraw-Hill Companies, Inc. Barnett/Ziegler/Byleen Precalculus: A Graphing Approach Chapter Six Trigonometric Identities & Conditional.
Copyright © 2009 Pearson Addison-Wesley Trigonometric Identities.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 2.6 Solving Equations: The Addition and Multiplication Properties.
TRIGONOMETRIC EQUATIONS Solving a Trigonometric Equation : 1. Try to reduce the equation to one involving a single function 2. Solve the equation using.
Copyright © 2007 Pearson Education, Inc. Slide 9-2 Chapter 9: Trigonometric Identities and Equations 9.1Trigonometric Identities 9.2Sum and Difference.
Copyright © 2009 Pearson Addison-Wesley Trigonometric Identities.
In this section, you will learn to:
Slide Fundamental Identities 5.2 Verifying Trigonometric Identities 5.3 Sum and Difference Identities for Cosine 5.4 Sum and Difference Identities.
Analytic Trigonometry Section 4.1 Trigonometric Identities
Section 7.5 Solving Trigonometric Equations Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.
Slide Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Verifying Trig Identities Today you will be verifying trigonometric identities to prove that a trigonometric equation is true for any replacement of the.
15.2 VERIFYING TRIG IDENTITIES.  Verifying trig identities algebraically involves transforming one side of the equation into the same form as the other.
Slide Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
1 © 2010 Pearson Education, Inc. All rights reserved © 2010 Pearson Education, Inc. All rights reserved Chapter 5 Analytic Trigonometry.
Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Section 2.1 The Addition Principle of Equality.
Section 5.5 Solving Exponential and Logarithmic Equations Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.
Verifying Trig Identities (5.1) JMerrill, 2009 (contributions from DDillon)
Trigonometric Identities
7.1 Trig Identities Simplifying Trig Expressions
Vocabulary identity trigonometric identity cofunction odd-even identities BELLRINGER: Define each word in your notebook.
Trig – Ch. 7-1 Proving Trig Identities Objectives: To understand how to verify an identity.
8 Copyright © Cengage Learning. All rights reserved. Analytic Trigonometry.
Chapter 5 Analytic Trigonometry Copyright © 2014, 2010, 2007 Pearson Education, Inc Verifying Trigonometric Identities.
1 © 2011 Pearson Education, Inc. All rights reserved 1 © 2010 Pearson Education, Inc. All rights reserved © 2011 Pearson Education, Inc. All rights reserved.
Copyright © 2005 Pearson Education, Inc.. Chapter 5 Trigonometric Identities.
Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1 6 Inverse Circular Functions and Trigonometric Equations.
Chapter 6 Analytic Trigonometry Copyright © 2014, 2010, 2007 Pearson Education, Inc Verifying Trigonometric Identities.
Copyright © Cengage Learning. All rights reserved. 5.2 Verifying Trigonometric Identities.
Holt McDougal Algebra 2 Fundamental Trigonometric Identities Fundamental Trigonometric Identities Holt Algebra 2Holt McDougal Algebra 2.
Trigonometric Identities
5 Trigonometric Identities.
Do Now Solve for x: 1. x + 3x – 4 = 2x – 7 2. (x + 1)2 – 3 = 4x + 1.
Analytic Trigonometry
Fundamental Trigonometric Identities Essential Questions
Chapter Seven Barnett/Ziegler/Byleen
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Section 6.1 Verifying Trigonometric Identities
Section 5.1 Verifying Trigonometric Identities
7.1 Trigonometric Identities
Fundamental Trigonometric Identities Essential Questions
Copyright © Cengage Learning. All rights reserved.
Copyright © 2017, 2013, 2009 Pearson Education, Inc.
7 Trigonometric Identities and Equations
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Copyright © 2017, 2013, 2009 Pearson Education, Inc.
Trigonometric Identities
Presentation transcript:

Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1 Inverse, Exponential, and Logarithmic Functions Copyright © 2013, 2009, 2005 Pearson Education, Inc. 7 Trigonometric Identities and Equations

Copyright © 2013, 2009, 2005 Pearson Education, Inc. 2 Verifying Trigonometric Identities 7.2 Strategies ▪ Verifying Identities by Working with One Side ▪ Verifying Identities by Working with Both Sides

Copyright © 2013, 2009, 2005 Pearson Education, Inc. 3 Verify Identities This section is about verifying identities. Really the question is: “Is the statement always true?” In order to answer this question we will try to use our identities to transform one side into the other.

Copyright © 2013, 2009, 2005 Pearson Education, Inc. 4 Caution The procedure for verifying identities is not the same as that of solving equations. Techniques used in solving equations, such as adding the same term to each side, and multiplying each side bythe same term, should not be used when working with identities.

Copyright © 2013, 2009, 2005 Pearson Education, Inc. 5 Verifying Identities by Working with One Side To avoid the temptation to use algebraic properties of equations to verify identities, one strategy is to work with only one side and rewrite it to match the other side.

Copyright © 2013, 2009, 2005 Pearson Education, Inc. 6 Hints for Verifying Identities  Learn the fundamental identities. Whenever you see either side of a fundamental identity, the other side should come to mind. Also, be aware of equivalent forms of the fundamental identities.  Try to rewrite the more complicated side of the equation so that it is identical to the simpler side.

Copyright © 2013, 2009, 2005 Pearson Education, Inc. 7 Hints for Verifying Identities  It is sometimes helpful to express all trigonometric functions in the equation in terms of sine and cosine and then simplify the result.  Usually, any factoring or indicated algebraic operations should be performed.

Copyright © 2013, 2009, 2005 Pearson Education, Inc. 8 Hints for Verifying Identities  As you select substitutions, keep in mind the side you are not changing, because it represents your goal. For example, to verify the identity find an identity that relates tan x to cos x. Since and the secant function is the best link between the two sides.

Copyright © 2013, 2009, 2005 Pearson Education, Inc. 9 Hints for Verifying Identities  If an expression contains 1 + sin x, multiplying both numerator and denominator by 1 – sin x would give 1 – sin 2 x, which could be replaced with cos 2 x. Similar procedures apply for 1 – sin x, 1 + cos x, and 1 – cos x.