Trig. Cheat Sheet
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1Trig. Cheat Sheet
(
) (
)
θ
θ
=
x y
,
cos ,sin
Definition of the Six Trigonometric Functions:
Interpreting the unit circle:
π
5
π
=
=
sin150
sin
0.5
θ
< <
0
6
Right triangle definitions, where
2
opp
.
hyp
.
θ
θ
=
=
sin
, csc
hyp
opp
.
adj
.
hyp
.
θ
θ
=
=
cos
, sec
hyp
.
adj
.
opp
.
adj
.
θ
θ
θ
=
=
tan
, cot
adj
.
opp
.
Defining the opposite and adjacent sides is dependent on the angle.
θ
Circular function definitions, where
is any angle in standard
=
+
>
2
2
position and
r
x
y
0.
y
x
y
r
r
x
θ
θ
θ
θ
θ
θ
=
=
=
=
=
=
. sin
, cos
, tan
, csc
,sec
, cot
r
r
x
y
x
y
θ
=
Double-Angle Formulas
Arc Length
s
r
Reciprocal Identities
2 tan
u
=
=
sin 2
u
2sin cos , tan 2
u
u
u
−
Law of Sines
1
1
1
2
1 tan
u
=
=
=
sin
u
cos
u
tan
u
=
−
sin
A
sin
B
SinC
csc
u
sec
u
cot
u
2
2
cos 2
u
cos
u
sin
u
=
=
a
b
c
1
1
1
=
−
2
=
=
=
2 cos
u
1
csc
u
sec
u
cot
u
sin
u
cos
u
tan
u
=
−
2
1 2sin
u
Law of Cosines
Power-Reducing Formulas
=
+
−
2
2
2
c
a
b
2
ab
cos
C
Tangent and Cotangent Identities
−
+
1 cos 2
u
1 cos 2
u
=
=
2
2
sin
u
, cos
u
sin
u
cos
u
=
=
tan
u
cot
u
2
2
DeMoivre’s Theorem
cos
u
sin
u
−
θ
θ
=
+
1 cos 2
u
n
n
Z
r
(cos
n
i
sin
n
)
=
2
tan
u
+
1 cos 2
u
Pythagorean Identities
Parabola:
+
=
+
=
2
2
2
2
sin
u
cos
u
1, 1 tan
u
sec
u
,
Half-angle Formulas
=
=
2
2
x
4 ,
ay y
4
ax
+
=
2
2
1 cot
u
csc
u
−
+
u
1 cos
u
u
1 cos
u
=
±
=
±
sin
, cos
2
2
2
2
2
2
x
y
Cofunction Identities
+
=
Ellipse:
1
−
−
2
2
π
π
a
b
u
1 cos
u
sin
u
1 cos
u
=
±
= =
=
−
=
−
tan
sin
u
cos , cos
u
u
sin
u
+
+
2
2
2
1 cos
u
1 cos
u
sin
u
x
y
2
2
−
=
Hyperbola:
1
2
2
π
π
a
b
=
−
=
−
csc
u
sec , sec
u
u
csc
u
2
2
π
π
=
−
=
−
π
π
π
tan
u
cot , cot
u
u
tan
u
×
=
→
×
= ≈
Deg. to Rad. deg.
radians
, 45
radians
, 45
0.7854
2
2
180
180
4
180
180
=
×
→
×
≈
Sum and Difference Formulas
Rad. to Deg.
rad
.
deg., 2.68
rad
.
deg., 2.68
153.55
π
π
=
±
±
sin(
u v
) sin cos
u
v
cos sin
u
v
±
=
cos(
u v
) cos cos
u
v
sin sin
u
v
Negative Angle Identites
±
−
= −
−
=
−
= −
tan
u
tan
v
sin(
u
)
sin , cos(
u
u
) cos , tan(
u
u
)
tan ,
u
±
=
tan(
u v
)
1 tan tan
u
v
−
= −
−
=
−
= −
csc(
u
)
csc , sec(
u
u
) sec , cot(
u
u
)
cot .
u
Tutoring Services, Chemeketa Community College, 4000 Lancaster Dr. NE, Salem, OR 97309.
Chemeketa Community College is an equal opportunity, affirmative action institution.
Revised 10/10
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