Double-Angle and Half-Angle Identities

Slides:



Advertisements
Similar presentations
Trigonometric Identities
Advertisements

Rev.S08 MAC 1114 Module 6 Trigonometric Identities II.
1 © 2010 Pearson Education, Inc. All rights reserved © 2010 Pearson Education, Inc. All rights reserved Chapter 5 Analytic Trigonometry.
DOUBLE-ANGLE AND HALF-ANGLE FORMULAS. If we want to know a formula for we could use the sum formula. we can trade these places This is called the double.
14-5 Sum and Difference of Angles Formulas. The Formulas.
Half Angle Formulas T, 11.0: Students demonstrate an understanding of half-angle and double- angle formulas for sines and cosines and can use those formulas.
In these sections, we will study the following topics:
Double-Angle and Half-Angle Identities Section 5.3.
Section 2 Identities: Cofunction, Double-Angle, & Half-Angle
Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 Objectives: Use the double-angle formulas. Use the power-reducing formulas. Use the half-angle formulas.
Section 5.5.  In the previous sections, we used: a) The Fundamental Identities a)Sin²x + Cos²x = 1 b) Sum & Difference Formulas a)Cos (u – v) = Cos u.
ANALYTIC TRIGONOMETRY
Multiple–Angle and Product–to–Sum Formulas
Trigonometry Cloud County Community College Spring, 2012 Instructor: Timothy L. Warkentin.
Verifying Trigonometric Identities
Lesson 14-1 Algebra Check Skills You’ll Need 14-4
Sections 14.6 &  Negative angle identities: ** the reciprocal functions act in the same way (csc, cot- move the negative out front; sec- can drop.
Copyright © Cengage Learning. All rights reserved. 5 Analytic Trigonometry.
Chapter 4 Analytic Trigonometry Section 4.3 Double-Angle, Half-Angle and Product- Sum Formulas.
Trig – 4/21/2017 Simplify. 312 Homework: p382 VC, 1-8, odds
6.2 Cofunction and Double-Angle Identities Fri Dec 5 Do Now Simplify (sinx + cosx)(sinx – cosx)
Chapter 4 Identities 4.1 Fundamental Identities and Their Use
5.1 Using Fundamental Identities. Fundamental Trigonometric Identities.
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.
Key Concept 1. Example 1 Evaluate Expressions Involving Double Angles If on the interval, find sin 2θ, cos 2θ, and tan 2θ. Since on the interval, one.
Double-Angle and Half-Angle Formulas
Copyright © 2009 Pearson Addison-Wesley Trigonometric Identities.
Double Angle Formulas T, 11.0: Students demonstrate an understanding of half-angle and double- angle formulas for sines and cosines and can use those formulas.
Using Trig Formulas In these sections, we will study the following topics: o Using the sum and difference formulas to evaluate trigonometric.
Using Trig Formulas In these sections, we will study the following topics: Using the sum and difference formulas to evaluate trigonometric.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 5- 1 Homework, Page 468 Use a sum or difference identity to find an.
Additional Identities Trigonometry MATH 103 S. Rook.
Further Trigonometric identities and their applications.
Solving Trigonometric Equations T, 11.0: Students demonstrate an understanding of half-angle and double- angle formulas for sines and cosines and can use.
6.5 Double-Angle and Half-Angle Formulas. Theorem Double-Angle Formulas.
Copyright © 2011 Pearson, Inc. Warm Up What is the Pythagorean Identity?
Copyright © Cengage Learning. All rights reserved.
Copyright © 2013, 2009, 2005 Pearson Education, Inc. 1 5 Trigonometric Identities.
Copyright © Cengage Learning. All rights reserved. 5 Analytic Trigonometry.
1 © 2011 Pearson Education, Inc. All rights reserved 1 © 2010 Pearson Education, Inc. All rights reserved © 2011 Pearson Education, Inc. All rights reserved.
Notes Over 7.5 Double-Angle Formulas Notes Over 7.5 Half-Angle Formulas.
Fundamental Trigonometric Identities Reciprocal Identities Tangent and Cotangent Identities Pythagorean Identities.
Sum and Difference Formulas Sum Formulas Sum and Difference Formulas Difference Formulas.
Section 7.3 Double-Angle, Half-Angle and Product-Sum Formulas Objectives: To understand and apply the double- angle formula. To understand and apply the.
Trig – 3/10/2016 Find the exact values of sin 2x, cos 2x, and tan 2x. 313 HW: p , 45, 47, 49, 51, 59, 61 Honors: 89, 91 Today’s Lesson: Half-Angle.
EXAMPLE 1 Evaluate trigonometric expressions Find the exact value of (a) cos 165° and (b) tan. π 12 a. cos 165° 1 2 = cos (330°) = – 1 + cos 330° 2 = –
10.1 – Sine & Cosine Formulas Sum & Difference Formulas.
Section 5.4. Double-Angle Identities Proving the first of these:
Then/Now You used sum and difference identities. (Lesson 5-4) Use double-angle, power-reducing, and half-angle identities to evaluate trigonometric expressions.
Chapter 6 Analytic Trigonometry Copyright © 2014, 2010, 2007 Pearson Education, Inc Double-Angle, Power- Reducing, and Half-Angle Formulas.
MULTIPLE ANGLE & PRODUCT –TO-SUM IDENTITIES Section 5-5.
Chapter 5 Analytic Trigonometry Multiple Angle Formulas Objective:  Rewrite and evaluate trigonometric functions using:  multiple-angle formulas.
1 Start Up Day 38 1.Solve over the interval 2. Solve:
Multiple-Angle and Product-Sum Formulas
Multiple – Angle Formulas
5.5 Multiple-Angle Formulas
Homework Lesson Handout
Use an addition or subtraction formula to find the exact value of the expression: {image} Select the correct answer: {image}
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Double- And Half-Angle Formulas
Copyright © Cengage Learning. All rights reserved.
DO NOW 14.6: Sum and Difference Formulas (PC 5.4)
5.4 Sum and Difference Formulas
Multiple-Angle and Product-to-Sum Formulas (Section 5-5)
Double-Angle and Half-Angle Formulas 5.3
Multiple-Angle and Product-to-Sum Formulas
Sum and Difference Formulas
Objective: Finding solutions of trigonometric equations.
Sum and Difference Formulas (Section 5-4)
Presentation transcript:

Double-Angle and Half-Angle Identities Section 5.3

Objectives Apply the half-angle and/or double angle formula to simplify an expression or evaluate an angle. Apply a power reducing formula to simplify an expression.

Double-Angle Identities

Half-Angle Identities

Power-Reducing Identities

Use a half-angle identity to find the exact value of

If find the values of the following trigonometric functions.

If find the values of the following trigonometric functions.

Use the power-reducing formula to simplify the expression Is there another way to simplify this without using a power-reducing formula?