ch 5 5 multiple angle and product to sum formulas l.
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Ch 5.5: Multiple-Angle and Product-to-Sum Formulas - PowerPoint PPT Presentation


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Ch 5.5: Multiple-Angle and Product-to-Sum Formulas. Double Angle Formulas. Half Angle Formulas. The + or – depends in which quadrant the original given value exists. 1. Draw a triangle. 2. Find the missing piece. Ex: Find the sin2 Ө and cos2 Ө if . 3. Use the formula.

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Presentation Transcript
slide2

Double Angle Formulas

Half Angle Formulas

The + or – depends in

which quadrant the original

given value exists

slide3

1. Draw a triangle

2. Find the missing

piece

Ex: Find the sin2Ө and cos2Ө if

3. Use the formula

slide4

1. Rewrite the inside as a sum

2. Use the formula from 5.4

Ex: Find the triple angle formula for:

3. Replace with double angle

formulas

4. Pythagorean Identity

5. Simplify

ex use the half angle formula to find the exact value of sin 105 o
Ex: Use the half angle formula to find the exact value of sin(105o)
  • 105 exists in the II, so sine is positive!

2. Double 105 to get

the numerator

3. Plug into the half formula

4.

5. Simplify

product to sum and sum to product formulas p379 p380 these will be provided on the test
Product-to-Sum and Sum-to-Product formulas: p379, p380 ***These will be provided on the test ***

Ex: Use the correct formula to write the following

product as a sum or difference:

1. Change using formula

2. Simplify

slide8

Ex: Find the exact value of

  • Change using sum-to-
  • product formula

2. Simplify

3. Use trig to

change cosines

4. Simplify