Basic Trigonometric Identities

Slides:

Advertisements

Similar presentations

Ch 5.2: Verifying Trig Identities. What are you doing? Trying to prove the left side equals the right side How do I do that? 1.Pick ONE SIDE to simplify.

Advertisements

Simplifying More Trig Expressions

Trigonometric Identities Section 4.3. Objectives Use algebra to simplify trigonometric expressions Establish 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.

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)

Identities and Equations  An equation such as y 2 – 9y + 20 = (y – 4)(y – 5) is an identity because the left-hand side (LHS) is equal to the right-hand.

Warm-Up: February 18, 2014 Write each of the following in terms of sine and cosine: tan x = csc x = sec x = cot x =

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 © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 4- 1 What you’ll learn about Identities Basic Trigonometric Identities.

5.1 Using Fundamental Identities. Fundamental Trigonometric Identities.

Pre calculus Problem of the Day Homework p odds Simplify the following:

Section 5.1 Verifying Trigonometric Identities.

In this section, you will learn to:

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.

6.2 Solving Trigonometric Equations with Identities.

MA L 7.2 Verifying Trigonometric Identities Make the left side equal the right.

November 7, 2012 Verifying Trig Identities Homework questions HW 5.2: Pg. 387 #4-36, multiples of 4.

1 © 2010 Pearson Education, Inc. All rights reserved © 2010 Pearson Education, Inc. All rights reserved Chapter 5 Analytic Trigonometry.

Verifying Trig Identities (5.1) JMerrill, 2009 (contributions from DDillon)

Sullivan PreCalculus Section 6.3 Trigonometric Identities

Trigonometric Identities

7.1 Trig Identities Simplifying Trig Expressions

Trig – Ch. 7-1 Proving Trig Identities Objectives: To understand how to verify an identity.

9.3 Trigonometric Identities. Two functions f and g are said to be identically equal if for every value of x for which both functions are defined. Such.

Chapter 7 Section 7.1 Fundamental Identities. Trigonometric Relations The six trigonometric functions are related in many different ways. Several of these.

MATHPOWER TM 12, WESTERN EDITION Chapter 5 Trigonometric Equations.

1 © 2011 Pearson Education, Inc. All rights reserved 1 © 2010 Pearson Education, Inc. All rights reserved © 2011 Pearson Education, Inc. All rights reserved.

10.1 – Sine & Cosine Formulas Sum & Difference Formulas.

MATH 1330 Section 5.1a. Trigonometric Functions of Real Numbers In this section there is nothing new as far as evaluating trigonometric functions. The.

Trigonometry Section 8.4 Simplify trigonometric expressions Reciprocal Relationships sin Θ = cos Θ = tan Θ = csc Θ = sec Θ = cot Θ = Ratio Relationships.

Pg. 407/423 Homework Pg. 407#33 Pg. 423 #16 – 18 all #9 tan x#31#32 #1x = 0.30, 2.84#2x = 0.72, 5.56 #3x = 0.98#4No Solution! #5x = π/6, 5π/6#6Ɵ = π/8.

Section Working With Trig Identities. Lesson Objective: Students will: Derive the other two Pythagorean identities. Verify trig identities.

Section 8-4 Relationships Among the Functions. Recall…

6.1A Reciprocal, Quotient, and Pythagorean Identities

Circular Functions & Trig Identities 3: Trigonometric Identities

TRIGONOMETRIC IDENTITIES

Sullivan Algebra and Trigonometry: Section 8.3

Section 5.1 Trigonometric Identities

Section 6.1 Verifying Trigonometric Identities

Section 5.1 Verifying Trigonometric Identities

MATH 1330 Section 4.4.

Lesson 5.1 Using Fundamental Identities

Basic Trigonometric Identities and Equations

5.2: Verifying Trigonometric Identities

6.3 Trigonometric Identities

Trigonometric Identities

One way to use identities is to simplify expressions involving trigonometric functions. Often a good strategy for doing this is to write all trig functions.

9.1 Identities and Proofs Identify possible identities by using graphs

Verifying Trigonometric Identities (Section 5-2)

Fundamental Identities

Basic Identities Trigonometric Identities Section 3.1

5.2 Verifying Trigonometric Identities

Warm-Up: February 3/4, 2016 Consider θ =60˚ Convert θ into radians

Lesson 1: Establishing Trig Identities

6.5 Basic Trigonometric Identities

Basic Trigonometric Identities and Equations

Trigonometric Identities

Trigonometric Identities

Trigonometric identities and equations Sum and difference identities

Basic Trigonometric Identities

Section 3.6 Basic Trigonometric Identities

Verifying Fundamental Identities

6.3 Trigonometric Identities

Take out a sheet of paper for the short quiz.

WArmup Rewrite 240° in radians..

Trigonometric Identities

Trigonometric Identities

Presentation transcript:

Basic Trigonometric Identities Section 15.1

Recall Basic Trig Identities

Pythagorean Identities

Strategy for Proving Identities Separate the equation into a left-side expression and right-side expression and work with these separately. Simplify the more complicated side, looking for ways to use the basic trig identities After simplifying one side as much as you can, try working with the other side until both sides are the same. Worst case scenario: express both sides in terms of sine and cosine. Then, clean up your mess. 

EXAMPLE: (note restrictions) Prove

EXAMPLE: (note Restrictions) Prove

EXAMPLE: (note Restrictions) Prove

EXAMPLE: (Note Restrictions) Prove:

Homework: p. 663-665, #9-27(odd)