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Formulas from geometry

A = area , V = Volume , and S = lateral surface area

The figure shows five geometric figures. The first is a parallelogram with height labeled as h and base as b. Below the figure is the formula for area, A = bh. The second is a triangle with height labeled as h and base as b. Below the figure is the formula for area, A = (1/2)bh.. The third is a trapezoid with the top horizontal side labeled as a, height as h, and base as b. Below the figure is the formula for area, A = (1/2)(a + b)h. The fourth is a circle with radius labeled as r. Below the figure is the formula for area, A= (pi)(r^2), and the formula for circumference, C = 2(pi)r. The fifth is a sector of a circle with radius labeled as r, sector length as s, and angle as theta. Below the figure is the formula for area, A = (1/2)r^2(theta), and sector length, s = r(theta) (theta in radians). The figure shows three solid figures. The first is a cylinder with height labeled as h and radius as r. Below the figure are the formulas for volume, V = (pi)(r^2)h, and surface area, S = 2(pi)rh. The second is a cone with height labeled as h, radius as r, and lateral side length as l. Below the figure are the formulas for volume, V = (1/3)(pi)(r^2)h, and surface area, S = (pi)rl. The third is a sphere with radius labeled as r. Below the figure are the formulas for volume, V = (4/3)(pi)(r^3), and surface area, S = 4(pi)r^2.

Formulas from algebra

Laws of exponents

x m x n = x m + n x m x n = x m n ( x m ) n = x m n x n = 1 x n ( x y ) n = x n y n ( x y ) n = x n y n x 1 / n = x n x y n = x n y n x y n = x n y n x m / n = x m n = ( x n ) m

Special factorizations

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 )

Quadratic formula

If a x 2 + b x + c = 0 , then x = b ± b 2 4 c a 2 a .

Binomial theorem

( a + b ) n = a n + ( n 1 ) a n 1 b + ( n 2 ) a n 2 b 2 + + ( n n 1 ) a b n 1 + b n ,

where ( n k ) = n ( n 1 ) ( n 2 ) ( n k + 1 ) k ( k 1 ) ( k 2 ) 3 2 1 = n ! k ! ( n k ) !

Formulas from trigonometry

Right-angle trigonometry

sin θ = opp hyp csc θ = hyp opp cos θ = adj hyp sec θ = hyp adj tan θ = opp adj cot θ = adj opp

The figure shows a right triangle with the longest side labeled hyp, the shorter leg labeled as opp, and the longer leg labeled as adj. The angle between the hypotenuse and the adjacent side is labeled theta.

Trigonometric functions of important angles

θ Radians sin θ cos θ tan θ
0 ° 0 0 1 0
30 ° π / 6 1 / 2 3 / 2 3 / 3
45 ° π / 4 2 / 2 2 / 2 1
60 ° π / 3 3 / 2 1 / 2 3
90 ° π / 2 1 0

Fundamental identities

sin 2 θ + cos 2 θ = 1 sin ( θ ) = sin θ 1 + tan 2 θ = sec 2 θ cos ( θ ) = cos θ 1 + cot 2 θ = csc 2 θ tan ( θ ) = tan θ sin ( π 2 θ ) = cos θ sin ( θ + 2 π ) = sin θ cos ( π 2 θ ) = sin θ cos ( θ + 2 π ) = cos θ tan ( π 2 θ ) = cot θ tan ( θ + π ) = tan θ

Law of sines

sin A a = sin B b = sin C c

The figure shows a nonright triangle with vertices labeled A, B, and C. The side opposite angle A is labeled a. The side opposite angle B is labeled b. The side opposite angle C is labeled c.

Law of cosines

a 2 = b 2 + c 2 2 b c cos A b 2 = a 2 + c 2 2 a c cos B c 2 = a 2 + b 2 2 a b cos C

Addition and subtraction formulas

sin ( x + y ) = sin x cos y + cos x sin y sin ( x y ) = sin x cos y cos x sin y cos ( x + y ) = cos x cos y sin x sin y cos ( x y ) = cos x cos y + sin x sin y tan ( x + y ) = tan x + tan y 1 tan x tan y tan ( x y ) = tan x tan y 1 + tan x tan y

Double-angle formulas

sin 2 x = 2 sin x cos x cos 2 x = cos 2 x sin 2 x = 2 cos 2 x 1 = 1 2 sin 2 x tan 2 x = 2 tan x 1 tan 2 x

Half-angle formulas

sin 2 x = 1 cos 2 x 2 cos 2 x = 1 + cos 2 x 2

Questions & Answers

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nandu
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Zakariya
evaluate the following computation (x³-8/x-2)
Murtala Reply
teach me how to solve the first law of calculus.
Uncle Reply
what is differentiation
Ibrahim Reply
f(x) = x-2 g(x) = 3x + 5 fog(x)? f(x)/g(x)
Naufal Reply
fog(x)= f(g(x)) = x-2 = 3x+5-2 = 3x+3 f(x)/g(x)= x-2/3x+5
diron
pweding paturo nsa calculus?
jimmy
how to use fundamental theorem to solve exponential
JULIA Reply
find the bounded area of the parabola y^2=4x and y=16x
Omar Reply
what is absolute value means?
Geo Reply
Chicken nuggets
Hugh
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MM
🐔🦃 nuggets
MM
(mathematics) For a complex number a+bi, the principal square root of the sum of the squares of its real and imaginary parts, √a2+b2 . Denoted by | |. The absolute value |x| of a real number x is √x2 , which is equal to x if x is non-negative, and −x if x is negative.
Ismael
find integration of loge x
Game Reply
find the volume of a solid about the y-axis, x=0, x=1, y=0, y=7+x^3
Godwin Reply
how does this work
Brad Reply
Can calculus give the answers as same as other methods give in basic classes while solving the numericals?
Cosmos Reply
log tan (x/4+x/2)
Rohan
please answer
Rohan
y=(x^2 + 3x).(eipix)
Claudia
is this a answer
Ismael
A Function F(X)=Sinx+cosx is odd or even?
WIZARD Reply
neither
David
Neither
Lovuyiso
f(x)=1/1+x^2 |=[-3,1]
Yuliana Reply
apa itu?
fauzi
determine the area of the region enclosed by x²+y=1,2x-y+4=0
Gerald Reply
Hi
MP
Hi too
Vic
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Adegoke
Which kind of pdf do you want bro?
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hi
Abdul
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Abdul
explain for me
Usman
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Fitzgerald
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Hamza

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Source:  OpenStax, Calculus volume 1. OpenStax CNX. Feb 05, 2016 Download for free at http://cnx.org/content/col11964/1.2
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