# Trigonometric Equations

## Contents

#### Terms

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.

#### Formulae

 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) .