pre-cal 40s slides october 26, 2007

13
Proofing PROOF continued ...

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Finish proving the angle sum and difference identities ... exercises.

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Page 2: Pre-Cal 40S Slides October 26, 2007

Proofs of the Sum and Difference Identities ...

Rotate ∠ROP so that OP lies on the positive x-axis

O O

Page 3: Pre-Cal 40S Slides October 26, 2007
Page 4: Pre-Cal 40S Slides October 26, 2007

Proofs of the Sum and Difference Identities ...

Rotate ∠ROP so that OP lies on the positive x-axis

O O

Page 5: Pre-Cal 40S Slides October 26, 2007

Recall the Even and Odd Identities

sin(-x) = -sin(x) cos(-x) = cos(x) tan(-x) = -tan(x)

The sine and tangent functions are ODD functions. Cosine is an EVEN function.

Page 6: Pre-Cal 40S Slides October 26, 2007

Recall the Even and Odd Identities

sin(-x) = -sin(x) cos(-x) = cos(x) tan(-x) = -tan(x)

The sine and tangent functions are ODD functions. Cosine is an EVEN function.

Page 7: Pre-Cal 40S Slides October 26, 2007

Now back to our regularly scheduled programming ...

Page 8: Pre-Cal 40S Slides October 26, 2007

How would you show this ...

Page 9: Pre-Cal 40S Slides October 26, 2007

How would you show this ...

Recall the Even and Odd Identities

sin(-x) = -sin(x) cos(-x) = cos(x) tan(-x) = -tan(x)

The sine and tangent functions are ODD functions. Cosine is an EVEN function.

Page 10: Pre-Cal 40S Slides October 26, 2007

Given: With and

Find

Page 11: Pre-Cal 40S Slides October 26, 2007

Given: With and

Find

Page 12: Pre-Cal 40S Slides October 26, 2007

Prove the following identity ...

Page 13: Pre-Cal 40S Slides October 26, 2007

Prove: