TRIGONOMETRY CHEAT SHEET
2
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→
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© Paul Dawkins -
https://tutorial.math.lamar.edu
Right triangle definition
Definition of the Trig Functions
Unit Circle Definition
For this definition we assume that
0
<
θ
<
π or 0
◦
<
θ
<
90
◦
.
2
For this definition θ is any angle.
sin(θ)
=
opposite
hypotenus
e
csc(θ) =
hypotenuse
opposite
sin(θ)
=
y
=
ycsc(θ)
=
1
cos(θ)
=
adjacent
sec(θ) = hypotenuse
1y
hypotenus
e
adjacen
t
cos(θ)
=
x
=
x
sec(θ) = 1
tan(θ) =
opposite
adjace
nt
cot(θ) =
adjacent
opposit
e
1
tan(θ) = y
x
x
cot(θ) = x
y
Domain
Facts and Properties
Period
The domain is all the values of θ that
can be plugged into the function.
sin(θ), θ can be any
angle cos(θ), θ can be
any angle
tan(θ), θ
n
+
1
π, n
=
0, ±1, ±2, . . .
The period of a function is the number, T ,
such
that
f
(θ
+
T )
= f
(θ). So, if ω is a
fixed number and θ is any angle we
have the following
periods.
sin (ω θ)
T
=
2π
ω
cos (ω θ)
T
=
2π
ω
csc(θ), θ /= nπ, n
=
0, ±1, ±2, . . . π
sec(θ), θ
n
+
1
2
π, n
=
0, ±1, ±2, . .
.
tan (ω θ)
→T
=
ω
2π
cot(θ), θ
nπ, n
=
0, ±1, ±2, . .
.
csc (ω θ)
→T
=
ω
2π
sec (ω θ)
→T
=
ω
Range
The range is all possible values to get out of the
function.
cot (ω θ)
T
=
π
ω
