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4.4 Compound Angle Formulas.notebook
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May 04, 2014
4.4: Compound Angle Formulas
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In the pages that follow, compound angle formulas will be developed using algebra and the unit circle
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The compound angle formulas for sine, cosine and tangent are:
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sin(x + y) = sin(x)cos(y) + cos(x)sin(y)
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sin(x ‐ y) = sin(x)cos(y) ‐ cos(x)sin(y)
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cos(x + y) = cos(x)cos(y) ‐ sin(x)sin(y)
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cos(x ‐ y) = cos(x)cos(y) + sin(x)sin(y)
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tan(x + y) = tan(x) + tan(y) / 1 ‐ tan(x)tan(y)
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tan(x ‐ y) = tan(x) ‐ tan(y) / 1 + tan(x)tan(y)
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By using compound angle formulas, you are able to determine exact values for trigonometric raos that can be expressed as the sum or difference of special angles.
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4.4 Compound Angle Formulas.notebook
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May 04, 2014
Proving the sum formula for cosine: cos(x+y)
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4.4 Compound Angle Formulas.notebook
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May 04, 2014
Proving the difference formula for cosine: cos(x ‐ y)
The subtracon formula for cosine can be derived from the addion formula for cosine:
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4.4 Compound Angle Formulas.notebook
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May 04, 2014
Proving the sum formula for sin(x + y)
Recall: Co‐funcon identes involving (90
0 ‐ x)
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4.4 Compound Angle Formulas.notebook
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May 04, 2014
Proving the difference formula for sin(x ‐ y)
The difference formula for sine can be derived from the sum formula for sine:
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4.4 Compound Angle Formulas.notebook
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May 04, 2014
Proving the sum formula for tan(x + y)
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4.4 Compound Angle Formulas.notebook
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May 04, 2014
Proving the difference formula for tan(x ‐ y)
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4.4 Compound Angle Formulas.notebook
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May 04, 2014
Example 1: Find the exact value of
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4.4 Compound Angle Formulas.notebook
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May 04, 2014
Example 2: If , , and
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evaluate
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Attachments
4.4 example 1.pdf
4.4 example 2.pdf
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SMART Notebook
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SMART Notebook
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