Trigonometry

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Trigonometry is the study of angles and triangles, relying heavily on three basic functions: sine, cosine and tangent, and their inverses, Cotangent (Cot), Secant (sec) and Cosecant (csc). These functions are abbreviated as "sin", "cos" and "tan".

These functions are defined by reference to a "right triangle," which is a triangle in which one angle is 90 degrees.

A right triangle
A way to remember the relationships is the mnemonic SOH-CAH-TOA ("soak a toe"). Think of a man soaking his toe in a tub of water - preferably a three-sided tub!
  • SOH: Sine = opposite over hypotenuse
  • CAH: Cosine = adjacent over hypotenuse
  • TOA: Tangent = opposite over adjacent

Formulas

Complementary formulas:

\sin(90^\circ-\alpha) \, = \, \cos\alpha
\cos(90^\circ-\alpha) \, = \, \sin\alpha

Pythagorean trigonometric identity:

\sin^2\alpha + \cos^2\alpha \, = 1

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