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TRIGONOMETRY


>Right triangle trigonometry


A right triangle is defined as having one angle precisely equal to 90o (a right angle).

Trigonometric identities


H is the Hypotenuse, always being opposite the right angle. Relative to angle x, O is the Opposite and A is the Adjacent.
“Arc” functions such as “arcsin”, “arccos”, and “arctan” are the complements of normal trigonometric functions. These functions return an angle for a ratio input. For example, if the tangent of 45o is equal to 1, then the “arctangent” (arctan) of 1 is 45o. “Arc” functions are useful for finding angles in a right triangle if the side lengths are known.

The Pythagorean theorem

Non-right triangle trigonometry

The Law of Sines (for any triangle)

The Law of Cosines

Trigonometric equivalencies

Hyperbolic functions


Note: all angles (x) must be expressed in units of radians for these hyperbolic functions. There are 2π radians in a circle (360o).