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The Double Angle Identities




          twins by luana
Proofs of the Sum and Difference Identities ...




                              Rotate ∠ROP so that OP        O
            O                 lies on the positive x-axis
Recall the Even and Odd Identities
 The sine and tangent functions are ODD functions.
 Cosine is an EVEN function.
  sin(-x) = -sin(x)        cos(-x) = cos(x)          tan(-x) = -tan(x)
Proofs of the Sum and Difference Identities ...




                              Rotate ∠ROP so that OP
            O                 lies on the positive x-axis   O
Recall the Even and Odd Identities
 The sine and tangent functions are ODD functions.
 Cosine is an EVEN function.
  sin(-x) = -sin(x)        cos(-x) = cos(x)          tan(-x) = -tan(x)
Pre-Cal 40S Slides March 27, 2008
Pre-Cal 40S Slides March 27, 2008
Pre-Cal 40S Slides March 27, 2008
Pre-Cal 40S Slides March 27, 2008
Pre-Cal 40S Slides March 27, 2008
Pre-Cal 40S Slides March 27, 2008
Pre-Cal 40S Slides March 27, 2008
Pre-Cal 40S Slides March 27, 2008

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Pre-Cal 40S Slides March 27, 2008

  • 1. The Double Angle Identities twins by luana
  • 2. Proofs of the Sum and Difference Identities ... Rotate ∠ROP so that OP O O lies on the positive x-axis
  • 3. Recall the Even and Odd Identities The sine and tangent functions are ODD functions. Cosine is an EVEN function. sin(-x) = -sin(x) cos(-x) = cos(x) tan(-x) = -tan(x)
  • 4. Proofs of the Sum and Difference Identities ... Rotate ∠ROP so that OP O lies on the positive x-axis O
  • 5. Recall the Even and Odd Identities The sine and tangent functions are ODD functions. Cosine is an EVEN function. sin(-x) = -sin(x) cos(-x) = cos(x) tan(-x) = -tan(x)