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# Review Sheet for MATH 104 with Professor Stylianou at KU

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This 5 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Kansas taught by a professor in Fall. Since its upload, it has received 19 views.

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Date Created: 02/06/15

All Formulas Distance Formula The distance between two points x1y1 and x2y2 is given by 2 1 x2 x12 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 gx fx gm f gx f x gx fgx xgx f x gx If gx 0 Minimum and Maximum Values of a Quadratic Function b A quadratic of the form axz 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 2x23x1 Example fx W 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 loga 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 CS09 600 x y x cot 0 y Trigonometric Functions on a Right Triangle ad sin0 cos0 J tan0 yp hyp J csc hyp 00th cote opp adj opp Fundamental Trigonometric Identities Reciprocal Identities sine cos0 tan0 csc 0 sec 0 cot 0 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 1cot20 cscz See Trigonometric Formulas Sheet for More Trig Identities Law of Sines a b c sinA sinB sinC Law of Cosines a2 b202 2bccosA 2 2 2 b a c 2accosB 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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