1300 Math Formulas by Golden Art.pdf
All Rights Reserved. http://fribok.blogspot.com/. Page 3. This handbook is a ... Formulas. 4.10. Double Angle Formulas. 4.11. Multiple Angle Formulas. 4.12. Half ...
Mathematical Formula Handbook.pdf
Speigel M.R.
1300 Math Formulas
1300 Math Formulas. ISBN 9949107741. Copyright © 2004 A.Svirin. All Rights Reserved. Page 3. This page is intentionally left blank. i. Page 4. Preface. This
1300 Math Formulas
Page 1. Page 2. 1300 Math Formulas. ISBN 9949107741. Copyright © 2004 A.Svirin. All Rights Reserved. Page 3. Preface mathematics. The ebook contains hundreds ...
BYJUS
The basic maths class 10 formulas are almost the same for all the boards. Download Class 10 Maths Formulas PDF Here: Linear Equations. One Variable ax+b=0 a ...
Differentiation Formulas Integration Formulas
Page 1. Differentiation Formulas d dx k = 0. (1) d dx. [f(x) ± g(x)] = f (x) ± g (x). (2) d dx. [k · f(x)] = k · f (x). (3) d dx. [f(x)g(x)] = f(
Mensuration and Mensuration Formulas PDF
You will study the mensuration formulas and properties of different geometric shapes and figures in maths in this article. Now let's learn all the important ...
Physical Science: Tables & Formulas
Type of reaction. Generalized formula. Specific Example. Combustion. HC + O2 → H2O + CO2. 2C2H6 + 7O2 → 6H2O + 4CO2. Synthesis. A + B → AB.
Mathcentre
so that the gradient of this line is 1. What about the equation y = 2x? This also represents a straight line and for all the points on the line each y value
INDEX MATHEMATICS FORMULA BOOKLET - GYAAN SUTRA
Fundamental of Mathematics Parametric Equations of a Circle: ... (Note that lateral surfaces of a prism are all rectangle). 15. Volume of a pyramid =.
MATH FORMULAS & FUNDAS
This eBook contains a list of formulas and concepts Arithmetic. Algebra. Geometry. Modern Math ... arranging all the observations from lowest value to.
FORMULAS FOR PERIMETER AREA
VOLUME
List MF19
List of formulae and statistical tables. Cambridge International AS & A Level. Mathematics (9709) and Further Mathematics (9231). For use from 2020 in all
Mensuration and Mensuration Formulas PDF
Mensuration is the branch of mathematics which studies the measurement of the Now let's learn all the important mensuration formulas involving 2D and 3D.
1300 Math Formulas
All Rights Reserved. math to math for advanced undergraduates in engineering ... contains hundreds of formulas
Mathematical Formula Handbook.pdf
Speigel M.R.
Formula Sheet 1 Factoring Formulas 2 Exponentiation Rules
Finally the quadratic formula: if a
Trigonometric Formula Sheet - Definition of the Trig Functions
Identities and Formulas Degrees to Radians Formulas ... These are all the solutions (including the complex values) of the equation x4 = 4.
BASIC GEOMETRIC FORMULAS AND PROPERTIES
For further or more advanced geometric formulas and properties consult with a SLAC counselor. r. Square: Perimeter: P = 4s or 2s + 2s. Area: A = s2.
Algebraic Formula Sheet - Middle Georgia State University
Algebraic Formula Sheet Algebraic Formula Sheet Arithmetic Operations ac bc = c(a + b) ! a = bc c ad + bc = bd b b b a = c d d c ab + ac = b + c; a 6 = 0 ! ab = c ac = ! b b c ad bc = d bd + b a b = + c c c ! ad ! = bc Properties of Exponents xnxm = xn+m (xn)m = xnm (xy)n = xnyn n 1 m x m
Trigonometric Formula Sheet
Denition of the Trig Functions
Right Triangle Denition
Assume that:
0< <2
or 0< <90hypotenuse adjacentopposite sin=opphyp csc=hypopp cos=adjhyp sec=hypadj tan=oppadj cot=adjoppUnit Circle DenitionAssumecan be any angle.xy
y x1(x;y) sin=y1 csc=1y cos=x1 sec=1x tan=yx cot=xyDomains of the Trig Functions
sin;82(1;1) cos;82(1;1) tan;86= n +12 ; where n2Zcsc;86=n; where n2Z sec;86= n+12 ; where n2Z cot;86=n; where n2ZRanges of the Trig Functions
1sin1 1cos11 tan 1csc1andcsc 1
sec1andsec 11 cot 1
Periods of the Trig Functions
The period of a function is the number, T, such that f (+T ) = f () . So, if!is a xed number andis any angle we have the following periods. sin(!))T=2! cos(!))T=2! tan(!))T=! csc(!))T=2! sec(!))T=2! cot(!))T=! 1Identities and Formulas
Tangent and Cotangent Identities
tan=sincoscot=cossinReciprocal Identities
sin=1csccsc=1sin cos=1secsec=1cos tan=1cotcot=1tanPythagorean Identities
sin2+ cos2= 1
tan2+ 1 = sec2
1 + cot
2= csc2
Even and Odd Formulas
sin() =sin cos() = cos tan() =tancsc() =csc sec() = sec cot() =cotPeriodic Formulas
If n is an integer
sin(+ 2n) = sin cos(+ 2n) = cos tan(+n) = tancsc(+ 2n) = csc sec(+ 2n) = sec cot(+n) = cotDouble Angle Formulas
sin(2) = 2sincos cos(2) = cos2sin2 = 2cos 21= 12sin2 tan(2) =2tan1tan2
Degrees to Radians Formulas
Ifxis an angle in degrees andtis an angle in
radians then: 180=tx )t=x180 andx=180tHalf Angle Formulas sin=r1cos(2)2 cos=r1 + cos(2)2 tan=s1cos(2)1 + cos(2)
Sum and Dierence Formulas
sin() = sincoscossin cos() = coscossinsin tan() =tantan1tantanProduct to Sum Formulas
sinsin=12 [cos()cos(+)] coscos=12 [cos() + cos(+)] sincos=12 [sin(+) + sin()] cossin=12 [sin(+)sin()]Sum to Product Formulas
sin+ sin= 2sin+2 cos2 sinsin= 2cos+2 sin2 cos+ cos= 2cos+2 cos2 coscos=2sin+2 sin2Cofunction Formulas
sin 2 = cos csc 2 = sec tan 2 = cotcos 2 = sin sec 2 = csc cot 2 = tan 2Unit Circle
0 ;2(1;0)180 ;(1;0)(0;1)90 ;2 (0;1)270 ;3230 ;6( p3 2 ;12 )45 ;4( p2 2 ;p2 2 )60 ;3( 12 ;p3 2 )120 ;23(12 ;p3 2 )135 ;34(p2 2 ;p2 2 )150 ;56(p3 2 ;12 )210 ;76 (p3 2 ;12 )225 ;54 (p2 2 ;p2 2 )240 ;43 (12 ;p3 2 )300 ;53 12 ;p3 2 )315 ;74 p2 2 ;p2 2 )330 ;116 p3 2 ;12 )For any ordered pair on the unit circle(x;y) : cos=x andsin=yExample
cos( 76) =p3 2 sin(76 ) =12 3
Inverse Trig Functions
Denition
= sin1(x)is equivalent tox= sin = cos1(x)is equivalent tox= cos = tan1(x)is equivalent tox= tanDomain and Range
Function
= sin1(x) = cos1(x) = tan1(x)Domain 1x1 1x11 x 1Range
2 2 0 2 < <2Inverse Properties
These properties hold for x in the domain andin
the range sin(sin1(x)) =x
cos(cos1(x)) =x
tan(tan1(x)) =xsin
1(sin()) =
cos1(cos()) =
tan1(tan()) =
Other Notations
sin1(x) = arcsin(x)
cos1(x) = arccos(x)
tan1(x) = arctan(x)
Law of Sines, Cosines, and Tangentsa
bcLaw of Sines
sina =sinb =sin cLaw of Cosines
a2=b2+c22bccos
b2=a2+c22accos
c2=a2+b22abcos
Law of Tangents
aba+b=tan12 ()tan 12 bcb+c=tan12 )tan 12 aca+c=tan12 )tan 12 4Complex Numbers
i=p1i2=1i3=i i4= 1 pa=ipa; a0 (a+bi) + (c+di) =a+c+ (b+d)i (a+bi)(c+di) =ac+ (bd)i (a+bi)(c+di) =acbd+ (ad+bc)i(a+bi)(abi) =a2+b2 ja+bij=pa2+b2Complex Modulus(a+bi) =abiComplex Conjugate(a+bi)(a+bi) =ja+bij2
DeMoivre's Theorem
Letz=r(cos+isin), and letnbe a positive integer.
Then: z n=rn(cosn+isinn):Example:Letz= 1i, ndz6.
Solution: First writezin polar form.
r=p(1)2+ (1)2=p2
=arg(z) = tan111 =4Polar Form:z=p2
cos 4 +isin 4Applying DeMoivre's Theorem gives :
z 6=p2 6 cos 6 4 +isin 6 4 = 2 3 cos 32+isin 32
= 8(0 +i(1)) = 8i 5 Finding thenthroots of a number using DeMoivre's Theorem Example:Find all the complex fourth roots of 4. That is, nd all the complex solutions of x 4= 4.
We are asked to nd all complex fourth roots of 4.
These are all the solutions (including the complex values) of the equationx4= 4. For any positive integern, a nonzero complex numberzhas exactlyndistinctnth roots. More specically, ifzis written in the trigonometric formr(cos+isin), thenth roots of zare given by the following formula. ()r1n cosn +360kn+isinn +360kn
; for k= 0;1;2;:::;n1: Remember from the previous example we need to write 4 in trigonometric form by using: r=p(a)2+ (b)2and=arg(z) = tan1ba
So we have the complex numbera+ib= 4 +i0.
Thereforea= 4 andb= 0
Sor=p(4)
2+ (0)2= 4 and
=arg(z) = tan104 = 0Finally our trigonometric form is 4 = 4(cos0
+isin0) Using the formula () above withn= 4, we can nd the fourth roots of 4(cos0+isin0)Fork= 0;414
cos04 +36004+isin04 +36004
=p2(cos(0 ) +isin(0)) =p2
Fork= 1;414
cos04 +36014+isin04 +36014
=p2(cos(90 ) +isin(90)) =p2i
Fork= 2;414
cos04 +36024+isin04 +36024
=p2(cos(180 ) +isin(180)) =p2
Fork= 3;414
cos04 +36034+isin04 +36034
=p2(cos(270 ) +isin(270)) =p2i
Thus all of the complex roots ofx4= 4 are:
p2;p2i;p2;p2i. 6Formulas for the Conic Sections
Circle
StandardForm: (xh)2+ (yk)2=r2
Where(h;k) =centerandr=radius
Ellipse
Standard Form for Horizontal Major Axis:
(xh)2a2+(yk)2b
2=1Standard Form for V ertical Major Axis:
(xh)2b2+(yk)2a
2=1Where (h;k)= center
2a=length of major axis
2b=length of minor axis
(0Foci can be found by usingc2=a2b2Wherec= foci length
7More Conic Sections
Hyperbola
Standard Form for Horizontal Transverse Axis:
(xh)2a2(yk)2b
2=1Standard Form for V ertical Transverse Axis:
(yk)2a2(xh)2b
2=1Where (h;k)= center
a=distance between center and either vertexFoci can be found by usingb2=c2a2
Wherecis the distance between
center and either focus. (b>0)Parabola
Vertical axis:y=a(xh)2+k
Horizontal axis:x=a(yk)2+h
Where (h;k)= vertex
a=scaling factor 8 xExample: sin(
(5π4 )=p22f(x)f(x) = sin(x)0π
6π 4π 3π -112⎷2
2⎷3
2 12 ⎷2 2 ⎷3 2xExample: cos(
(7π6 )=p32f(x)f(x) = cos(x)0π
6π 4π 3π -112⎷2
2⎷3
2 12 ⎷2 2 ⎷3 2 9 xf(x)f(x) = tanxπ 2- π2 ⎷331⎷3
⎷3 3 -1- ⎷3π 4-π40π
6-π6π
3-π32π3-
2π33π4-
3π45π6-
5π6π-π10
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