Sec' 7'2 Addition and Subtraction Formulas

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• Sec. 7.2 Addition and Subtraction Formulas
• Sec. 7.3 Double Angle, Half Angle Formulas

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Previous Trig Identities
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• Addition and Subtraction Formulas

For a visual proof of these see this web page.
The Book has an algebraic proof.
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• Addition and Subtraction Formulas

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• How to use Addition and Subtraction Formulas
• Use the following identity
• To show the cofunction identity

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• How to use Addition and Subtraction Formulas
• Using the values of the trig functions at certain
  angles, we can determine the values at new
  angles.

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• Double Angle Formulas

Proof
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• Formulas for Squares of Trig Functions

Proof Note What happens when you add the
formulas for sin2(x) and cos2(x)?
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• Half Angle Formulas

Proof
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• Applications
• 1. Find the exact value of

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• Applications
• 2. Suppose we know that for angle t,
  
• and t is in the 2nd quadrant.
• Find the values of sin for double that angle.

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• Applications
• 2. Suppose we know that for angle t,
  
• and t is in the 2nd quadrant.
• Find the values of sin for half that angle.

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• Applications
• 4. Suppose we know that for angle t,
  
• and t is in the 3rd quadrant.
• Find the values of sin for double that angle.

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• Applications
• 4. Suppose we know that for angle t,
  
• and t is in the 3rd quadrant.
• Find the values of sin for half that angle.