sparknotes
Trigonometric Equations
Terms and Formulae
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) . |
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