Trigonometry: Trigonometric Functions
Terms and Formulae
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) = 
.
|
