This document provides mathematical formulas and definitions for topics in algebra, geometry, trigonometry, and other areas of mathematics. It includes 3 or fewer sentences summarizing key information about triangles, circles, factoring polynomials, exponents, trigonometric functions, and other concepts. Diagrams illustrate formulas for areas of geometric shapes, trigonometric functions, and other visual representations. Tables list trigonometric function values at common angles in both radians and degrees.

1. P1: FCH/FFX
P2: FCH/FFX
GTBL001-front˙end
QC: FCH/FFX
T1: FCH
GTBL001-Smith-v16.cls
October 17, 2005
20:2
Algebra
Geometry
Arithmetic
Triangle
a+b
a
b
= +
c
c
c
a
b
c
d
=
a
b
Area = 1 bh
2
c2 = a 2 + b2 − 2ab cos θ
c
ad + bc
a
+ =
b
d
bd
d
c
=
Circle
Area = πr 2
C = 2πr
ad
bc
a
c
r
h
␪
b
Factoring
x 2 − y 2 = (x − y)(x + y)
x 3 − y 3 = (x − y)(x 2 + x y + y 2 )
x 3 + y 3 = (x + y)(x 2 − x y + y 2 )
x 4 − y 4 = (x − y)(x + y)(x 2 + y 2 )
Binomial
(x + y)2 = x 2 + 2x y + y 2
Sector of a Circle
Trapezoid
Area = 1 r 2 θ
2
s = rθ
(for θ in radians only)
Area = 1 (a + b)h
2
a
(x + y)3 = x 3 + 3x 2 y + 3x y 2 + y 3
h
s
Exponents
xn xm
x −n
=
b
xn
= x n−m
xm
x n+m
1
= n
x
x n/m =
√
m
(x y)n
√
n
xn
=
xy =
(x n )m
x
y
x n yn
√ √
n
xny
n
=
x nm
xn
= n
y
√
n
n
x
x
= √
n y
y
␪
r
Sphere
Cone
Volume = 4 πr 3
3
Surface Area = 4πr 2
Volume = 1 πr 2 h
3
√
Surface Area = πr r 2 + h 2
Lines
Slope m of line through (x0 , y0 ) and (x1 , y1 )
m=
r
h
y1 − y0
x1 − x0
r
Through (x0 , y0 ), slope m
y − y0 = m(x − x0 )
Slope m, y-intercept b
y = mx + b
Quadratic Formula
If ax 2 + bx + c = 0 then
x=
−b ±
√
b2 − 4ac
2a
Cylinder
Volume = πr 2 h
Surface Area = 2πr h
h
r
Distance
Distance d between (x1 , y1 ) and (x2 , y2 )
d=
(x2 − x1 )2 + (y2 − y1 )2
1

2. P1: FCH/FFX
P2: FCH/FFX
GTBL001-front˙end
QC: FCH/FFX
GTBL001-Smith-v16.cls
T1: FCH
October 17, 2005
20:2
Trigonometry
sin θ =
(x, y)
r
Half-Angle
y
r
sin2 θ =
x
cos θ =
r
␪
tan θ =
1 − cos 2θ
2
cos2 θ =
1 + cos 2θ
2
Addition
y
x
sin(a + b) = sin a cos b + cos a sin b
cos(a + b) = cos a cos b − sin a sin b
Subtraction
sin θ =
hyp
opp
cos θ =
adj
hyp
tan θ =
␪
sin(a − b) = sin a cos b − cos a sin b
opp
hyp
cos(a − b) = cos a cos b + sin a sin b
Sum
u−v
u+v
cos
2
2
u−v
u+v
cos
cos u + cos v = 2 cos
2
2
sin u + sin v = 2 sin
opp
adj
adj
Product
sin u sin v = 1 [cos(u − v) − cos(u + v)]
2
Reciprocals
cot θ =
1
tan θ
cos u cos v = 1 [cos(u − v) + cos(u + v)]
2
sec θ =
1
cos θ
csc θ =
1
sin θ
sin u cos v = 1 [sin(u + v) + sin(u − v)]
2
cos u sin v = 1 [sin(u + v) − sin(u − v)]
2
Definitions
π/2
2π/3
cos θ
cot θ =
sin θ
1
sec θ =
cos θ
1
csc θ =
sin θ
π/3
π/4
3π/4
5π/6
π
Pythagorean
sin2 θ + cos2 θ = 1
tan2 θ + 1 = sec2 θ
π/6
0
1 + cot2 θ = csc2 θ
Radians
sin(0) = 0
cos(0) = 1
− θ = cos θ
π
2
− θ = sin θ
π
2
− θ = cot θ
Even/Odd
sin(−θ ) = −sin θ
cos(−θ) = cos θ
tan(−θ ) = −tan θ
Double-Angle
sin 2θ = 2 sin θ cos θ
cos 2θ = cos2 θ − sin2 θ
π
3
=
π
2
sin
2π
3
=
3π
4
=
5π
6
=
=
π
3
=
1
2
π
2
=0
2π
3
= −1
2
cos
3π
4
=−
cos
1
2
π
4
√
3
2
√
2
2
cos
√
3
2
√
2
2
=
cos
1
2
√
2
2
√
3
2
π
6
cos
=1
sin
tan
=
sin
cos
π
4
sin
π
2
sin
sin
sin
=
cos
cos
sin
Cofunction
π
6
5π
6
=
2
2
√
− 23
sin(π) = 0
cos 2θ = 1 − 2 sin2 θ
cos(π ) = −1
sin(2π) = 0
cos(2π ) = 1
2
√