Prove and use Pythagorean identity

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Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
Guided Notes →One page your students fill in and keep.
Exit Ticket →Three items at the end of class. No student accounts.
Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
Homework →Assign practice; it grades itself.

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.

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

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

Review first:

Extend trigonometric functions using unit circle

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Pythagorean identity

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Exercise

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