Precalculus Last updated Mar 3, 2020 Page ID24051 Save as PDF word3.pg Analytic trigonometry Analytic trigonometryAddition & subtraction formulasDouble-angle & half-angle formulasProduct-to-sum & sum-to-product formulasSolving trigonometric equations exactlySolving trigonometric equations numericallyUsing and proving basic identitiesUsing and proving general identitiesShow allConic sectionsEllipsesHyperbolasIntersections of conicsParabolasPolar or parametric formExponential and logarithmic expressions and functionsApplications and models - population growthApplications and models - radioactive decayApplications and models – generalExponential and logarithmic equationsExponential functionsGraphsInequalitiesLogarithmic functionsProperties of logarithmsShow allFinite sequences and seriesArithmeticBinomial theoremNotationSummation formulasFunctionsCompositions and combinations of functionsDefinition, conceptDifference quotientDomain and rangeFunction notationGraphsInterpretation and applicationsPiecewise functionsShow allFunctions with fractional exponents and radical functionsApplicationsEquationsFunctions with fractional exponentsRadical functionsGeometric and algebraic foundations for trigonometryArc length, sector area, angular and linear velocityRadians, converting radians & degreesReference angles (using coterminal angles)Similar figuresThe Pythagorean theorem & its converseInverse functions1-1 functionsFinding the inverse functionInterpreting inverse functionsLinear equations and functionsApplications and modelsEquations of lines: generalEquations of lines: point-slope formEquations of lines: slope-intercept formEquations of lines: standard formFinding the slopeGraphs of linesLinear equationsLinear functionsLinear inequalitiesParallel and perpendicular linesShow allOperations on polynomial and rational expressionsPartial fractionsPolynomials: add, subtractPolynomials: dividePolynomials: multiplyRational expressions: add, subtractRational expressions: multiply, divideSimplify rational expressionsShow allPolar coordinates & vectorsCurvesInequalitiesPolar and rectangular coordinatesPolynomial equations and functionsApplications and modelsComplex rootsCounting zerosGraphs of polynomialsInequalities involving polynomialsPolynomial equationsPolynomial functionsRemainder and factor theoremsZeros and multiplicitiesShow allQuadratic equations and functionsApplications and modelsCompleting the squareComplex rootsForms: vertex, factored, generalGraphsInequalitiesQuadratic formulaSolve by factoringSolving equationsShow allRational equations and functionsApplications and modelsAsymptotesGraphs of rational functionsRational equationsRational functionsRational inequalitiesSimplifyingShow allSystems of equations and inequalitiesInequalitiesLinear systemsNonlinear systemsTransformations of functions and graphsHorizontal shiftsHorizontal stretches and compressionsReflectReflections and symmetryReflect and scale changeReflect and shiftScale changes: vertical and horizontalShifts: vertical and horizontalShift and scale changeSymmetry: even, odd, neitherThree or more transformationsVertical shiftsVertical stretches and compressionsShow allTriangle trigonometryApplications of special triangles & right trianglesSine, cosine, and tangent of an angle in a right triangleTrigonometric functionsCombinations and compositions of functionsInverse trigonometric functions - definitions, graphs, & propertiesModeling with trigonometric functionsSecant & cosecant functions - definitions, graphs, & propertiesSine & cosine functions - definitions, graphs, & propertiesTangent & cotangent functions - definitions, graphs, & propertiesTrigonometric functions of non-special anglesTrigonometric functions of special anglesUnit circleShow allVariation and power functionsApplications of power functionsDirect variationInverse variationMixed variationPower functions