<< Chapter < Page Chapter >> Page >

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

what is the limit of x^2+x when x approaches 0
Dike Reply
find derivatives 3√x²+√3x²
Care Reply
3 + 3=6
mujahid
How to do basic integrals
dondi Reply
write something lmit
ram Reply
find the integral of tan tanxdx
Lateef Reply
-ln|cosx| + C
Jug
discuss continuity of x-[x] at [ _1 1]
Atshdr Reply
Given that u = tan–¹(y/x), show that d²u/dx² + d²u/dy²=0
Collince Reply
find the limiting value of 5n-3÷2n-7
Joy Reply
Use the first principal to solve the following questions 5x-1
Cecilia Reply
175000/9*100-100+164294/9*100-100*4
Ibrahim Reply
mode of (x+4) is equal to 10..graph it how?
Sunny Reply
66
ram
6
ram
6
Cajab
what is domain in calculus
nelson
integrals of 1/6-6x-5x²
Namwandi Reply
derivative of (-x^3+1)%x^2
Misha Reply
(-x^5+x^2)/100
Sarada
(-5x^4+2x)/100
Sarada
oh sorry it's (-x^3+1)÷x^2
Misha
-5x^4+2x
Sarada
sorry I didn't understan A with that symbol
Sarada
find the derivative of the following y=4^e5x y=Cos^2 y=x^inx , x>0 y= 1+x^2/1-x^2 y=Sin ^2 3x + Cos^2 3x please guys I need answer and solutions
Ga Reply
differentiate y=(3x-2)^2(2x^2+5) and simplify the result
Ga
72x³-72x²+106x-60
okhiria
y= (2x^2+5)(3x+9)^2
lemmor
solve for dy/dx of y= 8x^3+5x^2-x+5
Ga Reply
192x^2+50x-1
Daniel
are you sure? my answer is 24x^2+10x-1 but I'm not sure about my answer .. what do you think?
Ga
24x²+10x-1
Eyad
eyad Amin that's the correct answer?
Ga
yes
Eyad
ok ok hehe thanks nice dp ekko hahaha
Ga
hahaha 😂❤️❤️❤️ welcome bro ❤️
Eyad
eyad please answer my other question for my assignment
Ga
y= (2x^2+5)(3x+9)^2
lemmor
can i join?
Fernando
yes of course
Jug
can anyone teach me integral calculus?
Jug
it's just the opposite of differential calculus
yhin
of coursr
okhiria
but i think, it's more complicated than calculus 1
Jug
Hello can someone help me with calculus one...
Jainaba

Get the best Calculus volume 1 course in your pocket!





Source:  OpenStax, Calculus volume 1. OpenStax CNX. Feb 05, 2016 Download for free at http://cnx.org/content/col11964/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Calculus volume 1' conversation and receive update notifications?

Ask