SECT 5.6 TRIGONOMETRICIDENTITIES PART 2

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DOUBLE ANGLE IDENTITIES

Verify the identities Numerically with:

The identityis valid

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PROVING THE DOUBLE ANGLE IDENTITIES

To prove the Double Angle Identities, use the “Sum Identities”

Ex: Prove

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PRACTICE: PROVE THE FOLLOWING IDENTITIES

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USING DOUBLE ANGLE IDENTITIES TO SOLVE EQUATIONS

Ex: Solve the following equation for 0 ≤ θ ≤ 360°

Note: You are “Solving for θ”,not proving an identity!!

Use the Double-Angle Identity

Factor the equation

Solve for θ from each equation.

Remember to use CAST and there

are TWO cycles between 0 and 360°

Add the period (180°) to find other solutions

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PRACTICE: SOLVE FOR 0 ≤ Θ ≤ 360°

Use the Double-Angle Identity

Factor: Difference of Square

Solve for θ from each equation.

Remember to use CAST

Note: There is only ONE cycle

Between 0 and 360°

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PROOFS USING DOUBLE ANGLE IDENTITIES

Use the Double-Angle Identity

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PRACTICE: PROVE THE FOLLOWING IDENTITIES

Multiply top &bottom by:

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CHALLENGE: PROVE

Sum Identities

Use the Double Angle Identities

for  “sin2x”  &  “cos2x”

Expand/Distribute

Combine like-terms

Pythagorean Identity

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CHALLENGE:

Graph the following equation without a graphing calculator.Find the amplitude, period, vertical and horizontal shifts

First: Simplify the equation

using the Double Angle Identity

Amplitude:

Period:

Vertical shift:

x

y











1

2

3

4

5

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HOMEWORK:

P342

# 5, 6, 10, 13, 16, 17, 19, 24, 26 27 - 29

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