Trigonometric Equations

Terms and Formulae

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Terms and Formulae

Conditional Equation

A trigonometric equation that is solved only by certain angles.
Domain

The set of all possible inputs of a function.
Inverse Trigonometric Relation

The relations arcsine, arccosine, arctangent, arccosecant, arcsecant, and arccotangent are the inverse of the trigonometric functions sine, cosine, tangent, cosecant, secant, and tangent, respectively. For example, another way to write x = sin(y) is y = arcsin(x) or y = sin^-1(x). For the inverse relations, the roles of x and y are reversed.
Inverse Trigonometric Function

An inverse relation in which the range is restricted such that there exists a one-to-one correspondence between inputs and outputs (numbers and angles, respectively). Inverse trigonometric functions are named exactly as inverse relations, except that the functions are capitalized. Example: arcsine is a relation; Arcsine is a function.
Range

The set of all possible outputs of a function.
Trigonometric Identity

A trigonometric equation that is solved by any angle.

arccosecant

y = arccosecant of x = arccsc(x) = csc^-1(x). Another way to write x = csc(y).

arccosine

y = arccosine of x = arccos(x) = cos^-1(x). Another way to write x = cos(y).

arccotangent

y = arccotangent of x = arccot(x) = cot^-1(x). Another way to write x = cot(y).

arcsecant

y = arcsecant of x = arcsec(x) = sec^-1(x). Another way to write x = sec(y).

arcsine

y = arcsine of x = arcsin(x) = sin^-1(x). Another way to write x = sin(y).

arctangent

y = arctangent of x = arctan(x) = tan^-1(x). Another way to write x = tan(y).