Triangle area = \(\frac{1}{2} base \times height\)

SOH CAH TOA

  • Sine = Opposite / Hypotenus
  • Cosine = Adjacent / Hypotenus
  • Tangent = Opposite / Adjacent

Fundamental Theorem of Trigonometry

trigonometric identities reciprocal identities co-function identities even-odd identities sum-difference formulas double angle formulas

right triangles

trigonometry of triangles

Pythagorean Theorem

\[a^2 + b^2 = c^2\]

In a right triangle with sides measuring a, b, and c, where side c is the opposite of the right angle

Triangle Inequality Theorem

If x, y, z \(\in \mathbb{R}\), then \(\lvert x-y \rvert \leq \lvert x-z \rvert + \lvert z-y \rvert\)

In short, the length of one side will never be greater than the sum of the other two sides on a triangle.

Unit Circle