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Chapter 5 Analytic Trigonometry 1
5.4 Sum & Difference Formulas Objectives: Use sum and difference formulas to evaluate trigonometric functions, verify identities, and solve trigonometric equations. 2
Consider This…. Determine whether each equation is true or false. Justify your answer. 3
Sum & Difference Formulas Sine Cosine 4 Signs are the same. Signs change.
Sum & Difference Formulas Tangent 5
Example 1 Find the exact value of cos 75 °. Check your answer with a calculator. 6
Example 2 Find the exact value of. 7
Example 3 Simplify. 8
Example 4 Find the exact value of sin (u + v) given where and where 9
Example 5 Prove the cofunction identity. 10
Example 6 Simplify each expression. 11
Example 7 Find all solutions of the equation in the interval [0, 2π). 12
Homework 5.4 Worksheet 5.4 13
Ch:7 Trigonometric Identities and Equations
Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1 5 Trigonometric Identities.
Onward to Section 5.3. We’ll start with two diagrams: What is the relationship between the three angles? What is the relationship between the two chords?
EXAMPLE 3 Simplify an expression Simplify the expression cos (x + π). Sum formula for cosine cos (x + π) = cos x cos π – sin x sin π Evaluate. = (cos x)(–1)
Simplify an expression
EXAMPLE 1 Evaluate inverse trigonometric functions Evaluate the expression in both radians and degrees. a.cos –1 3 2 √ SOLUTION a. When 0 θ π or 0° 180°,
In these sections, we will study the following topics:
Chapter 4 Analytic Trigonometry Section 4.3 Double-Angle, Half-Angle and Product- Sum Formulas.
WARM-UP Prove: sin 2 x + cos 2 x = 1 This is one of 3 Pythagorean Identities that we will be using in Ch. 11. The other 2 are: 1 + tan 2 x = sec 2 x 1.
Chapter 4 Identities 4.1 Fundamental Identities and Their Use
Copyright © Cengage Learning. All rights reserved. Analytic Trigonometry.
CHAPTER 7: Trigonometric Identities, Inverse Functions, and Equations
Chapter 6 Trig 1060.
5.4 Sum and Difference Formulas In this section students will use sum and difference formulas to evaluate trigonometric functions, verify identities, and.
Sum and Difference Formulas New Identities. Cosine Formulas.
1 © 2010 Pearson Education, Inc. All rights reserved © 2010 Pearson Education, Inc. All rights reserved Chapter 5 Analytic Trigonometry.
Vocabulary reduction identity. Key Concept 1 Example 1 Evaluate a Trigonometric Expression A. Find the exact value of cos 75°. 30° + 45° = 75° Cosine.
Copyright © 2009 Pearson Addison-Wesley Trigonometric Identities.
7.3 Sum and Difference Identities
Using Trig Formulas In these sections, we will study the following topics: o Using the sum and difference formulas to evaluate trigonometric.
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