# AP Calc study cards

 .remove_background_ad { border: 1px solid #555555; padding: .75em; margin: .75em; background-color: #e7e7e7; } .rmbg_image { max-height: 80px; } Area of a Triangle Area of a triangle (SAS Formula) Area of a trapeziod Area of a circle A=πr2 Curcumference of a circle C = 2πrC = πd Lateral surface area of a cylinder S = 2πrh Total surface area of a cylinder S = 2πrh + 2πr2 Surface of a sphere S = 4πr2 Volume of a prism V = bhB = Area of base Volume of a pyramid B = Area of Base Volume of a cylinder V = πr2h Volume of a cone πr2h Volume of a sphere V = 4/3πr2 Double angle identity for cos2x 1/2 (1+cos2x) Double angle identity for sin2x 1/2 (1-cos2x) sin(π/2 -x) cosx tan( tan (π/2 - x) cotx sec (π/2 - x) cscx cos2x + sin2x 1 1 + cot2x csc2x 1 + tan2x sec2x 1/ sinX cscX 1 / cosX secX 1 / tanX cotX sinx / cosx tanx cosx / sinx cotx sin2x 2sinXcosX cos2x (in terms of cosX and sinX) cos2x - sin2x cos2X (in terms of cosX) 2cos2X-1 cos2X (in terms of sinX) 1 - 2sin2X sin(-x) -sinx cos(-x) cosx tan(-x) -tanx law of sines a / sinA = b / sinB = c / sinC Law of cosines a2 = b2 + c2 -2bccosA logab = c ac = b log ( AB ) log A + log B log ( A / B ) log A - log B log Ax x log A ln e 1 ln 1 0 eln x x Pythagorean Theorem a2 + b2 = c2 Distance between points ( x1, y1 ) and ( x2, y2 ) Slope of the line between points ( x1, y1 ) and ( x2, y2 ) Point-Slope equation of a line y - y1 = m( x -x1 ) slope intercept equation of a line y = mx + b standard form of the equation of a line Ax + Bx = C Circle with center at point (h, k) and raduis r ( x - h )2 + ( y - k )2 = r2 ellipse Ax2 + By2 = C Hyperbola Ax2 - By2 = C Hyperbola with axes as asymptotes xy = k Parabola (vertical axis of symmetry) y = ax2 + bx + c Parabola (horizontal axis of symmetry) x = ay2 + by + c Domain of a function the set of all possible values of x for a functions Range of a function the set of all possible values of y for a function function symmetric across the y-axis f(-x) = f(x) Even functions f(-x) = -f(x) function symmetric through the origin f(-x) = -f(x) Odd Function f(-x) = -f(x) Quadratic formula (roots of y = ax2 +bx +c) Inverse of a function ( f o f--1)(x) =  x To graph the inverse of a function... reflect the graph of the function across the line y = x To find the equation of the inverse of a function interchange x and y, then solve the equation for y If point ( a,b ) lies on the inverse function f-1 then... point ( b,a ) lies on function f Inverse of y = ex y = ln x Inverse of y = lnx y = ex Line parallel to y = mx + b through point ( x1,y1 ) y - y1 = m ( x-x1 )ory = mx + b1, where b1 = (y1-mx1) Line perpendicular to y = mx + b through point ( x1,y1 )  or where  .remove_background_ad { border: 1px solid #555555; padding: .75em; margin: .75em; background-color: #e7e7e7; } .rmbg_image { max-height: 80px; } AuthorAnonymous ID165940 Card SetAP Calc study cards Descriptioncalculus Updated2012-08-14T01:01:55Z Show Answers