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Trigonometry: Trigonometric Functions

Terms and Formulae

Trigonometric Functions

Functions

Terms

Domain  -  The set of all possible inputs of a function.
Function  -  An operation that assigns a correspondence from elements of one set to elements of another set.
Period  -  The repeating interval of a periodic function; the period of a function is a real number.
Periodic Function  -  A function that repeats itself in regular intervals; it follows this equation: f (x + c) = f (x) , where c is a constant.
Range  -  The set of all possible outputs of a function.
Reference Angle  -  The positive acute angle formed between the terminal side of an angle and the x-axis.
Rule  -  The part of a function that dictates the exact correspondence between the elements of one set and the elements of another set.
Trigonometric Functions  -  There are six trigonometric functions: Sine, cosine, tangent, cosecant, secant, and cotangent.
Unit Circle  -  The circle whose center is at the origin and whose radius is one.

Formulae

 
Cosecant Given a point P(x, y) on the terminal side of an angle θ in standard position, distance d from the origin, cosecant(θ) = csc(θ) = .
 
Cosine Given a point P(x, y) on the terminal side of an angle θ in standard position, distance d from the origin, cosine(θ) = cos(θ) = .
 
Cotangent Given a point P(x, y) on the terminal side of an angle θ in standard position, cotangent(θ) = cot(θ) = .
 
Secant Given a point P(x, y) on the terminal side of an angle θ in standard position, distance d from the origin, secant(θ) = sec(θ) = .
 
Sine Given a point P(x, y) on the terminal side of an angle θ in standard position, distance d from the origin, sine(θ) = sin(θ) = .
 
Tangent Given a point P(x, y) on the terminal side of an angle θ in standard position, tangent(θ) = tan(θ) = .

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