High School · Trigonometric Functions

CCSS.MATH.CONTENT.HSF.TF.C.8

Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.

Read this standard on the official Common Core site

Lessons that teach this standard

• The Pythagorean Identity: sin²θ + cos²θ = 1

  Why the Pythagorean theorem on the unit circle gives sin²θ + cos²θ = 1, what makes it an identity, and how to find sine, cosine or tangent from one value and a quadrant.

• Double-Angle and Half-Angle Formulas

  Derive sin 2θ, cos 2θ and tan 2θ from the sum formulas, reverse them into half-angle and power-reducing forms, and use them for exact values and equations.

• Verifying Trigonometric Identities

  Prove that two trigonometric expressions agree for every angle: work one side at a time, rewrite in sines and cosines, and trade with the Pythagorean identities.