This document contains a summary of key concepts in algebra, geometry, and trigonometry: 1) Algebra topics include arithmetic operations, factoring, exponents, binomials, and the quadratic formula. 2) Geometry topics cover lines, triangles, circles, spheres, cones, cylinders, sectors, and trapezoids including formulas for area, perimeter, volume, and surface area. 3) Trigonometry definitions and formulas are provided for sine, cosine, tangent, cotangent, addition, subtraction, and half-angle identities.

1. P1: FCH/FFX P2: FCH/FFX QC: FCH/FFX T1: FCH
GTBL001-front˙end GTBL001-Smith-v16.cls October 17, 2005 20:2
Algebra Geometry
Arithmetic Triangle Circle
a+b a b a c ad + bc Area = 1 bh Area = πr 2
= + + = 2
c c c b d bd c2 = a 2 + b2 − 2ab cos θ C = 2πr
a
b a d ad
= = a
c b c bc c r
h
d
␪
b
Factoring
x 2 − y 2 = (x − y)(x + y) x 3 − y 3 = (x − y)(x 2 + x y + y 2 ) Sector of a Circle Trapezoid
x 3 + y 3 = (x + y)(x 2 − x y + y 2 ) x 4 − y 4 = (x − y)(x + y)(x 2 + y 2 )
Area = 1 r 2 θ
2 Area = 1 (a + b)h
2
s = rθ
Binomial (for θ in radians only) a
(x + y)2 = x 2 + 2x y + y 2 (x + y)3 = x 3 + 3x 2 y + 3x y 2 + y 3
h
s
Exponents b
xn ␪
xn xm = x n+m = x n−m (x n )m = x nm
xm r
n
1 x xn
x −n = n (x y)n = x n yn = n
x y y Sphere Cone
√
√ √ √ √ x x n
x n/m = m
xn n xy = n
xny n = √ Volume = 4 πr 3 Volume = 1 πr 2 h
y n y
3 3 √
Surface Area = 4πr 2 Surface Area = πr r 2 + h 2
Lines
Slope m of line through (x0 , y0 ) and (x1 , y1 )
r
h
y1 − y0
m=
x1 − x0
r
Through (x0 , y0 ), slope m
y − y0 = m(x − x0 )
Slope m, y-intercept b
Cylinder
y = mx + b Volume = πr 2 h
Surface Area = 2πr h
Quadratic Formula
If ax 2 + bx + c = 0 then
√
−b ± b2 − 4ac h
x=
2a 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 QC: FCH/FFX T1: FCH
GTBL001-front˙end GTBL001-Smith-v16.cls October 17, 2005 20:2
Trigonometry
(x, y) sin θ =
y Half-Angle
r
1 − cos 2θ 1 + cos 2θ
r sin2 θ = cos2 θ =
x 2 2
cos θ =
␪ r
y
Addition
tan θ =
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 =
opp sin(a − b) = sin a cos b − cos a sin b cos(a − b) = cos a cos b + sin a sin b
hyp
hyp adj Sum
opp cos θ =
hyp u+v u−v
sin u + sin v = 2 sin cos
2 2
opp u+v u−v
tan θ = cos u + cos v = 2 cos cos
␪ adj 2 2
adj
Product
sin u sin v = 1 [cos(u − v) − cos(u + v)]
2
Reciprocals cos u cos v = 1 [cos(u − v) + cos(u + v)]
2
1 1 1 sin u cos v = 1 [sin(u + v) + sin(u − v)]
2
cot θ = sec θ = csc θ =
tan θ cos θ sin θ cos u sin v = 1 [sin(u + v) − sin(u − v)]
2
Definitions π/2
2π/3 π/3
cos θ 1 1 π/4
cot θ = sec θ = csc θ = 3π/4
sin θ cos θ sin θ
5π/6 π/6
Pythagorean π 0
sin2 θ + cos2 θ = 1 tan2 θ + 1 = sec2 θ 1 + cot2 θ = csc2 θ Radians
sin(0) = 0 cos(0) = 1
√
π π
Cofunction sin 6 = 1
2 cos 6 = 2
3
√ √
π π
π π π sin = 2
cos = 2
sin 2 − θ = cos θ cos 2 − θ = sin θ tan 2 − θ = cot θ 4 2 4 2
√
π π
sin 3 = 2
3
cos 3 = 1
2
π π
sin =1 cos =0
Even/Odd 2
√
2
sin 2π
3 = 2
3
cos 2π
3 = −1
2
sin(−θ ) = −sin θ cos(−θ) = cos θ tan(−θ ) = −tan θ √ √
sin 3π
4 = 2
2
cos 3π
4 =− 2
2
√
sin 5π
6 = 1
2 cos 5π
6 = − 23
Double-Angle sin(π) = 0 cos(π ) = −1
sin 2θ = 2 sin θ cos θ cos 2θ = cos2 θ − sin2 θ cos 2θ = 1 − 2 sin2 θ sin(2π) = 0 cos(2π) = 1
2