Terms and Formulae
Terms
Conditional Equation
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A trigonometric equation that is solved only by certain angles.
Domain
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The set of all possible inputs of a
function.
Inverse Trigonometric Relation
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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
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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
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The set of all possible outputs of a
function.
Trigonometric Identity
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A trigonometric equation that is solved by any angle.
Formulae
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arccosecant
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y = arccosecant of x = arccsc(x) = csc-1(x). Another way to write
x = csc(y).
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arccosine
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y = arccosine of x = arccos(x) = cos-1(x). Another way to write
x = cos(y).
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arccotangent
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y = arccotangent of x = arccot(x) = cot-1(x). Another way to write
x = cot(y).
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arcsecant
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y = arcsecant of x = arcsec(x) = sec-1(x). Another way to write
x = sec(y).
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arcsine
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y = arcsine of x = arcsin(x) = sin-1(x). Another way to write
x = sin(y).
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arctangent
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y = arctangent of x = arctan(x) = tan-1(x). Another way to write
x = tan(y).
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