Appendix B

Appendix B
SOME MATHEMATICAL FORMULAS
Geometry
C = 2r
A = r2
A = 4r2
V = 4 r3
3
V = r2h
Circumference of circle
Area of circle
Area of sphere
Volume of sphere
Volume of cylinder
Algebra
xnxm = x(n + m)
xn = x(n  m)
xm
1 =x
1/x
(xn)m = xnm
x1/m = (x)1/m
xn/m = (xn)1/m = (x1/m)n
(x + y)2 = x2 + 2xy + y2
(x  y)2 = x2  2xy + y2
(x + y)3 = x3 + 3x2y + 3xy2 + y3
(x  y)3 = x3  3x2y + 3xy2  y3
(x + y)(x  y) = x2  y2
Sums and Differences of the
Trigonometric Functions
sin(A + B) = sinA cosB + cosA sinB
sin(A  B) = sinA cosB  cosA sinB
cos(A + B) = cosA cosB  sinA sinB
Addition and Subtraction of the
Trigonometric Functions
sinA + sinB = 2 sin(A + B) cos(A  B)
2
2
sinA  sinB = 2 cos(A + B) sin(A  B)
2
2
cosA + cosB = 2 cos(A + B) cos(A  B)
2
2
cosA  cosB = 2 sin(A + B) sin(A  B)
2
2
Quadratic Equation
if ax2 + bx + c = 0
then
x
b  b2  4ac
2a
Binomial Expansion
(1 + x)n = 1 + nx + n(n  1)x2
2!
+ n(n  1)(n  2)x3 + ...
3!
Trigonometry
Figure B An obtuse triangle.
Law of Sines
a = b = c
sinA sinB sinC
Law of Cosines
c2 = a2 + b2  2ab cosC
Some Important Trigonometric Identities
sin2 + cos2 = 1
sec2 = 1 + tan2
csc2 = 1 + cot2
To go to the Table of Contents
click on this sentence.
B-1