2017_2018版高中数学第三章三角恒等变形3二倍角的三角函数一课件北师大版必修

North ChinaNormalUniversity EditionHighSchool MathematicsChapter3TrigonometricIdentities3Double-AngleTrigonometric FunctionsPart1Explore theconcept ofdouble-angle andlearn aboutits geometricalsignificance.Discover thecommonly usedformulas andlearn how they are derived.What isDouble-AngleFind outwhat double-angle means,how tocalculate it,and how to defineit geometrically.Definition CalculationGeometric MeaningDouble-angle refersto Thevalue ofthe double-The double-angle can bethe measurementof an angle can be calculatedgeometricallyangle thatis twiceas using the trigonometricrepresented as the anglelargeasthe original formulas.between twolines thatangle.It iscommonly intersectat thevertex,denoted as2αin witheach linemakingmathematical formulas.anangleofαwithrespect tothe horizontal.Common Double-Angle FormulasLearnabout thecommonly useddouble-angle formulasand understand howtheyarederived.1$sin2α=2sinαcosα$This formulaexpresses the sine ofthe double-angle interms ofthesineandcosine ofthe originalangle.It can be derived using the angle sum formula.2$cos2α=cos^2α-sin^2α$This formulaexpresses the cosine ofthe double-angle interms ofthecosineandsine ofthe originalangle.It canalso be derivedusingtheangle sumformula.3$tan2α=\dfrac{2tanα}{1-tan^2α}$This formulaexpresses thetangent ofthe double-angle interms ofthe tangentoftheoriginalangle.It canbederivedusingthehalf-angle formula.Deriving Double-Angle FormulasLearnhowto derive the double-angle formulasusing variousmathematical techniques.Pythagorean TheoremAngle Sum Formula Half-Angle FormulaThePythagorean TheoremThe AngleSumFormulaThe Half-Angle Formulacanbe used to derivethe canbe used to derivethe canbe usedtoderivethedouble-angle formulafor double-angle formulafor double-angle formulaforsine.cosine.tangent.Applications of Double-Angle FormulasDiscoverthe practicalapplications ofdouble-angle formulasandhowthey canbe usedto solveproblems.Angle AdditionFormulaThe angleaddition formulacanbederived fromthe double-angle formulaand usedto solveproblemsthat involvethe sumof twoangles.Special ValuesThedouble-angle formulacanbeusedtofind thevalues ofthe trigonometricfunctions forspecificangles,such asπ/4andπ/

3.Identity TransformationsThedouble-angle formulacanbeusedtotransform trigonometricidentities andequations.Important RemindersGettips andreminders tomake themost ofdouble-angle formulasand avoidcommon mistakes.•Double-angle formulasare primarilyused insolving problemsrelated toangles.•Be familiarwith theconversion betweendegree andradian.•Practice regularlyand checkfor accuracy.•Master theanglesumand half-angle formulasbefore learningthedouble-angle formula.SummaryRecap thekey conceptsand formulascovered inthis presentation.Concept FormulaDefinitionofDouble-Angle-Calculation ofDouble-Angle-Sine ofDouble-Angle$sin2α=2sinαcosα$Cosine ofDouble-Angle$cos2α=cos^2α-sin^2α$Tangent ofDouble-Angle$tan2α=\dfrac{2tanα}{1-tan^2α}$。