Double-Angle and Half-angle Formulas

Slides:

Advertisements

Similar presentations

Trigonometric Identities

Advertisements

Unit 5 Sum and Difference Identities. Finding Exact Value While doing this it is important to remember your 30, 45, and 60 degree angles. Also know each.

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

Evaluating Sine & Cosine and and Tangent (Section 7.4)

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.

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:

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.

Sum and Difference Formulas New Identities. Cosine Formulas.

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.

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.

Chapter 5 Analytic Trigonometry Sum & Difference Formulas Objectives:  Use sum and difference formulas to evaluate trigonometric functions, verify.

Solving Trigonometric Equations T, 11.0: Students demonstrate an understanding of half-angle and double- angle formulas for sines and cosines and can use.

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

Aim: What are the identities of sin (A ± B) and tan (A ±B)? Do Now: Write the cofunctions of the following 1. sin 30  2. sin A  3. sin (A + B)  sin.

EXAMPLE 1 Use an inverse tangent to find an angle measure Use a calculator to approximate the measure of A to the nearest tenth of a degree. SOLUTION Because.

(a) To use the formulae sin (A B), cos (A B) and tan (A B). (b) To derive and use the double angle formulae (c) To derive and use the half angle formulae.

Double-Angle and Half-Angle Identities

Double and Half Angle Formulas

DOUBLE-ANGLE AND HALF-ANGLE FORMULAS

9-3: Other Identities.

5 Trigonometric Identities.

Section 5.5B Half Angle Formulas

5.4 Sum and Difference Formulas

1.4 Trigonometric Functions of Any Angle

5.5/5.6 – Double- and Half-Angle Identities

Sum and Difference Identities

Use an addition or subtraction formula to find the exact value of the expression: {image} Select the correct answer: {image}

Double-Angle, Half-Angle, and Product-Sum Formulas

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

Pre-AP Pre-Calculus Chapter 5, Section 3

5.3/5.4 – Sum and Difference Identities

Ch 5.5: Multiple-Angle and Product-to-Sum Formulas

9.3 Double-Angle and Half-Angle Formulas

Find sin 2x, cos 2x, and tan 2x from the given information: {image} Select the correct answer:

Trigonometric Equations with Multiple Angles

Double- And Half-Angle Formulas

5-3 Tangent of Sums & Differences

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

7 Trigonometric Identities and Equations

Product-to-Sum and Sum-to-Product Formulas

Review Find the EXACT value of: 1. sin 30° 2. cos 225° 3. tan 135° 4. cos 300° How can we find the values of expressions like sin 15° ?? We need some new.

Copyright © 2017, 2013, 2009 Pearson Education, Inc.

Aim: What are the double angle and half angle trig identities?

Objectives Students will learn how to use special right triangles to find the radian and degrees.

Examples Double Angle Formulas

Revision Find the exact values of the following

Warm-Up: April 12, 2016 Use the sin⁡(

cos 2A = 1 – 2 sin² A or cos 2A = 2 cos² A – 1.

Multiple-Angle and Product-to-Sum Formulas (Section 5-5)

Double-Angle and Half-Angle Formulas 5.3

21. Sum and Difference Identities

Copyright © 2017, 2013, 2009 Pearson Education, Inc.

Double and Half Angle Formulas

Power-reducing & Half angle identities

Have homework out to be checked!!

5.5-Multiple Angle Formulas

Double-Angle, Half-Angle Formulas

Sum and Difference Formulas

5.5 Multiple Angle & Product-to-Sum Formulas

15. Sum and Difference Identities

7.3 Sum and Difference Identities

5.2 Sum and Difference Formulas

Objective: Use power-reducing and half angle identities.

5.4 Sum and Difference Identities

Sum and Difference Formulas (Section 5-4)

What is the radian equivalent?

Presentation transcript:

Double-Angle and Half-angle Formulas

Double-Angle Formulas

Finding exact values

Solutions

Solutions

solutions

Establishing Identities Develop a formula for sin (3θ) in terms of sin θ and cos θ.

Other variations of double-angle formulas

Establishing an identity Write an equivalent expression for cos^4θ that does not involve any powers of sine or cosine greater than 1.

Solution

Half angle formulas

Finding Exact Values Find the exact value of cos (15 degrees) Find the exact value of sin (165 deg) Find the exact value of tan (195 deg)

Finding Exact Values Remember to be careful to check the sign of the cosine of the angle Remember to look at the quadrant to determine if the final answer is positive or negative

Finding Exact Values

Solutions

alternative formula

On-line help Tutorial Video Help