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# Precalculus Mathematics MATH 104

KU

GPA 3.6

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This 5 page Class Notes was uploaded by Edgar Jacobi on Monday September 7, 2015. The Class Notes belongs to MATH 104 at Kansas taught by Antonis Stylianou in Fall. Since its upload, it has received 22 views. For similar materials see /class/182362/math-104-kansas in Mathematics (M) at Kansas.

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Date Created: 09/07/15

All Formulas Distance Formula The distance between two points x1y1 and x2y2 is given by 2 2 1 3 2 x1 Y2 Y1 Midpoint Formula The midpoint between two points x1y1 and x2y2 is given by x 39xz Y1Y2 2 2 39 Equation of a Circle The equation of acircle with radius r and Center hk is given by x h2y k2 r2 Quadratic Formula For a polynomial of the form axz bx c 0 the solutions for X are given by b 4172 4610 2a 5 Slope The clope of a nonvertical line through the points x1y1 and x2y2 is given by Y2Y1 x2x1 m PointSlope Equation of a Line The equation of a line passing through the point x1y1 with slope m is given by y Y1 mxx1 SlopeIntercept Equation of a Line The equation of a line with slope m and yintercept b is given by ymxb Combinations of Functions f 8x x 8x f gx f x gx f x f xgx we x if x 0 gj gx g Minimum and Maximum Values of a Quadratic Function 2 b A quadratic of the form ax bx c 0 has a minimum or a maXImum at x 2 a Vertical Asymptotes To find the vertical asymptotes of a rational function 1 Factor the top and the bottom 2 Cancel if possible 3 Set whatever is left on the bottom equal to O 4 Any results that you get are vertical asymptotes Note Vertical asymptotes have the form x Horizontal Asymptotes To find the horizontal asymptotes of a rational function look at the highest power on top and bottom f top bottom Create a fraction from the leading coefficients 2 2 3 1 Example fx x7 x The power on top is 2 and the power on bottom is 2 Since they are equal we form the fraction from the leading coefficients Thus we have a horizontal 2 asymptote at y 7 If top lt bottom There is a horizontal asymptote at y 0 If top gt bottom There is no horizontal asymptote Note Horizontal asymptotes have the form y Converting logs to exponents If loguxb then ab 6 Converting exponents to logs If ab xthen10guxb Properties of Logarithms 1 10guuv 10ga u10guv loguu loguv 10gauv u u 2 10gu 10ga u logu v log 14 loguv 10gu v v 3 logu uquot nlogu u nlogu u 10guuquot Converting Radians to Degrees 180 radians39 J deg rees 1 Converting Degrees to Radians degrees39 n J radians 180 Trigonometric Functions on the Unit Circle If 0 xy then sin0y cos0x tan0l X 1 csc secs i x y x cot 0 y Trigonometric Functions on a Right Triangle ad sin0 cos0 J tan0 hyp adj cs00hy p 00th cote pp adj opp Fundamental Trigonometric Identities Reciprocal Identities sine cos0 1 tan0 csc 0 sec 0 cot 0 1 1 1 cs00 600 cote s1n 0 cos 0 tan0 Quotient Identities tan0 sum cot 0 cfm 9 cos0 s1n 0 Pythagorean Identities sin2 0 cos2 01 1 tan2 0 S602 0 1 cot2 0 csc2 0 See Trigonometric Formulas Sheet for More Trig Identities Law of Sines a b c sinA sinB sinC Law of Cosines a2 b202 2bccosA b2 a2 02 2ac cosB 02 a2 b2 ZabcosC See Parabolas Ellipses and Hyperbolas sheets for information on conic sections Classifying a Conic The graph of sz Cy2 Dx Ey F 0 is one of the following 1 Circle A C 2 Parabola AC 0 3 Ellipse AC gt 0 4 Hyperbola AC lt 0 Converting Polar Coordinates to Rectangular Coordinates If given the polar coordinates r the rectangular coordinates are given by xy where x rcos0 and y rsin0 Converting Rectangular Coordinates to Polar Coordinates If given the rectangular coordinates xy one set of polar coordinates is given by r where r2 x2 y2 and tame 1 Another set of coordinates can be found by adding 2n to X 0

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