Common Core Math
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Learning Goal

Part of: Prove and apply trigonometric identities — 2 of 2 cluster items

Prove angle sum formulas

HSF.TF.C.9

**HSF.TF.C.9**: (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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HSF.TF.C.9: (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

What you'll learn

  1. State the angle addition formulas: sin(A + B) = sin(A)cos(B) + cos(A)sin(B) and cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
  2. Follow a geometric proof of cos(A - B) using the distance formula on the unit circle
  3. Derive sin(A + B) from cos(A + B) using the co-function relationship sin(theta) = cos(pi/2 - theta)
  4. Use the addition formulas to find exact values of non-standard angles (e.g., sin(75 degrees) = sin(45 + 30))
  5. Derive the double angle formulas as special cases: sin(2A) = 2 sin(A)cos(A) and cos(2A) = cos^2(A) - sin^2(A)
  6. Derive the tangent addition formula tan(A + B) = (tan(A) + tan(B))/(1 - tan(A)tan(B))

Slides

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Slides

In development

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