Precalculus: Trigonometric Functions
Terms and Formulae
Terms
Amplitude
-
One-half the distance between the minimun and maximum value of a periodic
function.
Coterminal
-
Having the same terminal side (a property of angles).
Identity
-
An equation containing one or more trigonometric functions which are true
regardless of the angle used.
Initial Side
-
The side of an angle from which the rotation begins, or the initial position of
the ray whose rotation creates the angle.
Inverse Trigonometric Function
-
The inverses of the six trigononometric
functions with specific restricted ranges. They are arcsine,
arccosine, arctangent, arccosecant, arcsecant, and
arccotangent.
Period
-
The repeating interval of a periodic function;
the period of a function is a real number.
Quadrant
-
One of the four regions in the coordinate plane created by the intersection of
the axes.
Quadrantal Angle
-
An angle in standard position whose terminal side lies along one of the
axes.
Radian
-
A unit of measure for angles. One revolution equals
2Π
radians. A radian
is also the measure of the central angle that intercepts an arc of the same
length as the radius.
Reference Angle
-
The positive acute angle formed between the terminal side of an angle and
the x-axis.
Standard Position
-
The location of an angle such that its vertex lies at the origin and its
initial side lies along the positive x-axis.
Terminal Side
-
The side of an angle after rotation; the final position of the ray whose
rotation created an angle.
Trigonometric Functions
-
Sine, cosine, tangent, cosecant, secant, and cotangent
are the six trigonometric functions.
Vertex
-
The common endpoint of two rays that form an angle.
Formulae
| arccosecant | y = arccsc(x) = csc -1(x) . Another way to write x = csc(y) . |
| arccosine | y = arccos(x) = cos -1(x) . Another way to write x = cos(y) . |
| arccotangent | y = arccot(x) = cot -1(x) . Another way to write x = cot(y) . |
| arcsecant | y = arcsec(x) = sec -1(x) . Another way to write x = sec(y) . |
| arcsine | y = arcsin(x) = sin -1(x) . Another way to write x = sin(y) . |
| arctangent | y = arctan(x) = tan -1(x) . Another way to write x = tan(y) . |
| Cosecant |
Given a point
P(x, y)
on the terminal side of an angle
θ
in
standard position, distance
d
from the origin, its cosecant is
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, its cosine is
cos(θ) = 
.
|
| Cotangent |
Given a point
P(x, y)
on the terminal side of an angle
θ
in
standard position, its cotangent is
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, its secant is
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, its sine is
sin(θ) = 
.
|
| Tangent |
Given a point
P(x, y)
on the terminal side of an angle
θ
in
standard position, its tangent is
tan(θ) =  = 
.
|
