Common Core Math
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Learning Goal

Part of: Prove and apply trigonometric identities — 1 of 2 cluster items

Prove and use Pythagorean identity

HSF.TF.C.8

**HSF.TF.C.8**: Prove the Pythagorean identity sin^2(theta) + cos^2(theta) = 1 and use it to find sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the angle.

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HSF.TF.C.8: Prove the Pythagorean identity sin^2(theta) + cos^2(theta) = 1 and use it to find sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant of the angle.

What you'll learn

  1. Prove that sin^2(theta) + cos^2(theta) = 1 using the unit circle equation x^2 + y^2 = 1
  2. Explain why this identity holds for all values of theta, not just acute angles
  3. Use the Pythagorean identity to find sin(theta) given cos(theta), or vice versa
  4. Determine the correct sign of the missing value using the quadrant of the angle
  5. Find tan(theta) given sin(theta) or cos(theta) and the quadrant
  6. Derive the related identities tan^2(theta) + 1 = sec^2(theta) and 1 + cot^2(theta) = csc^2(theta) by dividing through

Slides

Interactive presentations perfect for visual learners • Interactive presentation

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Pythagorean Identity

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Pythagorean Identity

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Exercises

Practice problems to build fluency and understanding • 1 exercises

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Exercises

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