Using Sum, Difference, and Double-Angle Identities

Sep 25, 2012

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Using Sum, Difference, and Double-Angle Identities

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Double-Angle and Half-Angle Identities

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.

2.32k views • 35 slides

7.2.1 – Sum and Difference Identities

7.2.1 – Sum and Difference Identities. A new set of identities we will deal with will allow us to determine exact trig values of angles on the unit circle that we do not know Example: sin(35 0 )?. Motivation allows us to avoid calculator use, and be more precise when talking of applied terms

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Sum and Difference Identities

Sum and Difference Identities. T, 11.0 Students demonstrate an understanding of half-angle and double-angle formulas for sines and cosines and can use those formulas to prove and/or simplify other trigonometric identities. . Sum and Difference Identities. Objectives. Key Words:.

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Sum and Difference Identities

Sum and Difference Identities. Using the sum and difference identities for sine, cosine, and tangent functions. Sum and Difference Identities for the Cosine Function. If α and β represent the measures of two angles, then the following identities hold for all values of α and β . .

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M A L7.3 Sum and Difference Identities

M A L7.3 Sum and Difference Identities. Sum and Difference formulas.

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Double-Angle and Power-Reducing Identities

Double-Angle and Power-Reducing Identities. Section 5.4. Double-Angle Identities. Proving the first of these:. Power-Reducing Identities. Guided Practice. Prove the given identity. Guided Practice. Prove the given identity. Guided Practice. Prove the given identity. Guided Practice.

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7.3 Sum and Difference Identities

7.3 Sum and Difference Identities. Previous Identities. Reciprocal Identities Quotient Identities Pythagorean Identities Negative-Number Identities Note It will be necessary to recognize alternative forms of the identities

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DOUBLE-ANGLE AND HALF-ANGLE IDENTITIES

DOUBLE-ANGLE AND HALF-ANGLE IDENTITIES. If we want to know a formula for we could use the sum formula. . we can trade these pla ces. This is called the double angle formula for sine since it tells you the sine of double x. Let's try the same thing for .

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Double-Angle and Half Angle Identities

Double-Angle and Half Angle Identities. Double-Angle Identity. If represents the measure of an angle, then the following identities hold for all values of . If and terminates in the first quadrant, find the exact value of each function. -1.

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7-3 Sum and Difference Identities!!

7-3 Sum and Difference Identities!!. What’s the point?. Even using the symmetry identities (Cases 1-4) which can transform our angles into Quadrant I, we don’t always end up with one of our special angles (0, 30, 45, 60, 90)

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Using Sum, Difference, and Double-Angle Identities

Chapter 5 Trigonometric Equations. 5.5. Using Sum, Difference, and Double-Angle Identities. 5.5. 1. MATHPOWER TM 12, WESTERN EDITION. Sum and Difference Identities. sin( A + B ) = sin A cos B + cos A sin B sin( A - B ) = sin A cos B - cos A sin B

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Sum and Difference Identities

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

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6.1 Sum & Difference Identities

6.1 Sum & Difference Identities. All the identities we learned in Ch 4 were with one angle We have identities that involve more than 1 angle! Question: Can we do this? sin 90° = sin (60° + 30°) Let’s check…. sin 90° = 1 So…. NO!. = sin 60° + sin 30°. sin 60° + sin 30° =.

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4.3 Sum, Difference, and Cofunction Identities

4.3 Sum, Difference, and Cofunction Identities. Sum and difference identities for cosine Cofunction identities Sum and difference identities for sine and tangent Summary and use. Sum and Difference Identities for Cosine. cos(x – y) = cos x cos y - sin x sin y Claim: cos( p /2 – y) = siny

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Double-Angle and Half-Angle Identities

1 2. = 2 – Replace with exact values. = – Simplify. 3 2. 3 2. Double-Angle and Half-Angle Identities. ALGEBRA 2 LESSON 14-7. Use a double-angle identity to find the exact value of sin 600°. sin 600° = sin 2(300°) Rewrite 600 as 2(300).

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9.3 Double-Angle and Half-Angle Formulas -FURTHER IDENTITIES

9.3 Double-Angle and Half-Angle Formulas -FURTHER IDENTITIES. Double Angle Formulas. Suppose we use the sum formula for sine, but the two values that we add are the same, that is α = β. Double angle formula for cosine. Alternate forms of the cosine double angle formula.

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7.2.2 – Sum and Difference Identities, Cont’d

7.2.2 – Sum and Difference Identities, Cont’d. Yesterday, we were able to cover the basics of the sum and difference identities for the basic trig functions Rewrite angles in terms of angles we know Express unknown angles in a new way Exact values.

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6.3 Double-Angle & Half-Angle Identities

6.3 Double-Angle & Half-Angle Identities. The Double-Angle Identities can be easily derived from the sum identities • • OR OR •. Double Angle Identities Half-Angle Identities. Examples: Find the exact values Ex 1) Find.  QII so (+). Ex 2) Given. –5. θ. –12.

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6.2 Sum, Difference, and Double Angle Identities

6.2 Sum, Difference, and Double Angle Identities. The expressions sin (A + B) and cos (A + B) occur frequently enough in math that it is necessary to find expressions equivalent to them that involve sines and cosines of single angles. So…. Does sin (A + B) = Sin A + Sin B.

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5.3 Sum and Difference Identities

5.3 Sum and Difference Identities. HW: PG. Pg. 468-469 #1-20 e, 24. Cosine of a Difference Identity. Using the cosine-of-a-difference identity. Find the exact value of cos15° without using a calculator. Cosine of a Sum. Cos(u + v) =. Cosine of a Sum or Difference.

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Using Sum, Difference, and Double-Angle Identities

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

Double-Angle, Half-Angle, and Product-Sum Formulas. The identities we consider in this section are consequences of the addition formulas. The Double-Angle Formulas allow us to find the values of the trigonometric functions at 2 x from their values at x .

387 views • 24 slides

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Using Sum, Difference, and Double-Angle Identities

Using Sum, Difference, and Double-Angle Identities

Presentation Transcript

Double-Angle and Half-Angle Identities

7.2.1 – Sum and Difference Identities

Sum and Difference Identities

Sum and Difference Identities

M A L7.3 Sum and Difference Identities

Double-Angle and Power-Reducing Identities

7.3 Sum and Difference Identities

DOUBLE-ANGLE AND HALF-ANGLE IDENTITIES

Double-Angle and Half Angle Identities

7-3 Sum and Difference Identities!!

Using Sum, Difference, and Double-Angle Identities

Sum and Difference Identities

6.1 Sum &amp; Difference Identities

4.3 Sum, Difference, and Cofunction Identities

Double-Angle and Half-Angle Identities

9.3 Double-Angle and Half-Angle Formulas -FURTHER IDENTITIES

7.2.2 – Sum and Difference Identities, Cont’d

6.3 Double-Angle &amp; Half-Angle Identities

6.2 Sum, Difference, and Double Angle Identities

5.3 Sum and Difference Identities

Using Sum, Difference, and Double-Angle Identities

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

6.1 Sum & Difference Identities

6.3 Double-Angle & Half-Angle Identities