Lone Star College-CyFair Formula Sheet

1 lone star College-CyFair Formula Sheet The following formulas are critical for success in the indicated course. Student CANNOT bring these formulas on a Formula Sheet or card to tests and instructors MUST NOT provide them during the test either on the board or on a handout. They MUST be memorized. Math 1314 college Algebra FORMULAS/EQUATIONS Distance Formula If 1=( 1, 1) and 2=( 2, 2), the distance from 1 to 2 is ( 1, 2)= ( 2 1)2+( 2 1)2 Standard Equation Of a Circle The standard equation of a circle of radius with center at ( , ) is ( )2+( )2= 2 Slope Formula The slope of the line containing the points 1=( 1, 1) and 2=( 2, 2) is = 2 1 2 1if 1 2 is undefinedif 1= 2 Point-slope Equation of a Line The equation of a line with slope containing the points ( 1, 1) is 1= ( 1) Slope-Intercept Equation of a Line The equation of a line with slope and -intercept is = + Quadratic Formula The solutions of the equation 2+ + =0, 0, are = 2 4 2 LIBRARY OF FUNCTIONS Constant Function ( )= Identity Function ( )= Square Function ( )= 2 Cube Function ( )

2 = 3 Reciprocal Function ( )=1 Squared Reciprocal Function ( )=1 2 Square Root Function ( )= Cube Root Function ( )= 3 Absolute Function ( )=| | Exponential Function ( )= Natural Logarithm Function ( )=ln Greatest Integer Function ( )= ( , ) ( , ) , ( )= ( )= ( , ) , ( , ) ( )= GEOMETRY FOMULAS Circle =Radius, =Area, =Circumference = = Triangle =Base, =Altitude(Height), =Area = Rectangle =Length, =Width, =Area, =Perimeter = = + Rectangular Box =Length, =Width, =Height, =Volume, =Surface Area = = + + PROPERTIES OF LOGARITHMS log ( )=log +log log ( )=log log log = log log =log log =ln ln = ln b h r Math 1316 Trigonometry Students in Trigonometry should know all the formulas from Math 1314 college Algebra plus the following.

3 Unit Circle + = TRIGONOMETRIC FUNCTIONS Of an Acute Angle sin = =OppositeHypotenuse csc = =HypotenuseOpposite cos = =AdjacentHypotenuse sec = =HypotenuseAdjacent tan = =OppositeAdjacent cot = =AdjacentOpposite Of a General Angle sin = csc = , 0 cos = sec = , 0 tan = , 0 cot = , 0 APPLICATIONS Arc Length: = , in radians Area of Sector: =12 2 , in radians Angular Speed: = , in radians Linear Speed: = , = SOLVING TRIANGLES Law of Sine: sin =sin =sin Law of Cosine: 2= 2+ 2 2 cos 2= 2+ 2 2 cos 2= 2+ 2 2 cos = + ( , ) b TRIGONOMETRIC IDENTITIES Fundamental Identities tan =sin cos cot =cos sin csc =1sin sec =1cos cot =1tan sin2 +cos2 =1 1+tan2 =sec2 1+cot2 =csc2 Even-Odd Identities Cofunction Identities sin( )= sin csc( )= csc cos( )=cos sec( )=sec tan( )= tan cot( )= cot cos(90 )=sin sin(90 )=cos tan(90 )=tan Sum and Difference Formulas Double-Angle Formulas sin( + )=sin cos +cos sin sin( )=sin cos cos sin cos( + )=cos cos sin sin cos( )=cos cos +sin sin tan( + )=tan +tan 1 tan tan tan( )=tan tan 1+tan tan sin(2 )=2sin cos cos(2 )=cos2 sin2 =2cos2 1 =1 2sin2 tan(2 )

4 =2tan 1 tan2 LIBRARY OF TRIGONOMETRIC FUNCTIONS Sine Function ( )=sin Cosine Function ( )=cos Tangent Function ( )=tan Secant Function ( )=sec Cosecant Function ( )=csc Cotangent Function ( )=cot Math 2412 Precalculus Students in Precalculus should know all the formulas from Math 1314 college Algebra and Math 1316 Trigonometry plus the following. Half Angle Formulas sin = 1 cos2 2 cos = 1+cos2 2 tan =1 cos2 sin2 Products and Quotients of Complex Numbers in Polar Form Let 1= 1(cos 1+ sin 1) and 2= 2(cos 2+ sin 2). Then 1 2= 1 2[cos( 1+ 2)+ sin( 1+ 2)] and, if 2 0, 1 2= 1 2[cos( 1 2)+ sin( 1 2)]. DeMoivre s Theorem If = (cos + sin ) and n is a positive integer, = [cos( )+ sin( )]. Complex Roots Let = (cos 0+ sin 0) be a complex number and let n 2be an integer.

5 If 0, there are n distinct complex nth roots of , given by the Formula = [cos 0 +2 + sin 0 +2 ]. Where =0,1,2, , 1. CONICS Circle + = Parabola = = = = Ellipse + = , > , 2= 2 2 + = , > , 2= 2 2 Hyperbola = , 2= 2+ 2 Asymptote: = , = = , 2= 2+ 2 Asymptote: = , = ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) : = ( , ) : = ( , ) : = ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) : = ( , ) POLAR EQUATIONS OF CONICS(Focus at the Pole, Eccentricity ) Equation Description = 1 cos Directrix is perpendicular to the polar axis at a distance units to the left of the pole.

6 = = 1+ cos Directrix is perpendicular to the polar axis at a distance units to the right of the pole: = = 1+ sin Directrix is parallel to the polar axis at a distance units above the pole: = = 1 sin Directrix is parallel to the polar axis at a distance units below the pole: = Eccentricity If =1, the conic is a parabola; the axis of symmetry is perpendicular to the directrix. If 0< <1, the conic is an ellipse; the major axis is perpendicular to the directrix. If >1, the conic is a hyperbola; the transverse axis is perpendicular to the directrix. ARITHMETIC SEQUENCE = 1+( 1) = 1+( 1+ )+( 1+2 )+ +[ 1+( 1) ] = 2[2 1+( 1) ] = 2[ 1+ ] GEOMETRIC SEQUENCE = 1 1 = 1+ 1 + 1 2+ + 1 1 = 1(1 )1 GEOMETRIC SERIES If | |<1, 1+ 1 + 1 2+ = 1 1 =1= 11 If | | 1, the infinite geometric series does not have a sum.

7 PERMUTATIONS/COMBINATIONS 0!=1 1!=1 != ( 1) (3)(2)(1) ( , )= !( )! C(n,r)=( )= !( )! ! BINOMIAL THEOREM ( + ) = +( 1) 1+( 2) 2 2+ +( 1) 1 +