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Math · Intermediate

Trigonometric Identities

Sine and cosine are bound by beautiful relationships. See why sin⁡2θ+cos⁡2θ=1\sin^2\theta + \cos^2\theta = 1, derive the angle-addition formulas, square sine waves with double angles, find the angle between lines, hear beats in a sum of waves, learn to prove and disprove identities, and solve trig equations with all their solutions.

8 lessons~45 min0/8 complete
Start courseHelpful background: Trigonometry
1

Core Identities

From the unit circle.

  1. The Pythagorean Identitysin² + cos² = 1
  2. Angle Additionsin(A + B) and cos(A + B)
  3. Double & Half AnglesSquares of sines are waves too
2

Using Identities

Waves and equations.

  1. Tangent & SlopesThe angle between two lines
  2. Adding Sine and CosineAlways another sine wave
  3. Products, Sums & BeatsTurning products into sums and back
  4. Proving IdentitiesStrategy, and testing claims
  5. Solving Trig EquationsFinding every solution