Teaching objectives - Oxfordshire Mathematics Community
Y13 A level Mathematics23 Trigonometry3 lessonsTeaching objectivesaIntroduction to radiansbSmall angle approximationscUsing exact values in radiansResources for advance preparation:StarterMain teachingIncluding key questions, key teaching points, models and resourcesNotesIncluding Support and ExtensionConsolidation/PlenaryIncluding key questions and homework1Create any angle measure and discuss arbitrary nature of degrees AngiesFinding angle where arc length = rDefinition of a radian as ratio of arc length to radiusWorking with radians to solve problems eg finding arc lengthAlternatively, link this unit with unit 30, and introduce radian measure in the context of differentiating trig functions, using a graph plotter.Calculating area of sectors, segments, and arc lengths I radians.2Identifying standard angles in radians.Using exact valuesFind exact values for sin, cos, tan of standard angles (in radians (fractions of pi))Using the correct notation for radian measureFractions of π0.3 radCheck solution(s) are in the correct range0 - 2 π- π - πSwitching between rad / deg on calculatorUsing exact values to solve problems Questions / Answers3Using a table to show that x = Sin x for small values of x and showing graphically. TableProof of Sin (x) = x using isosceles triangle, sector, right angle triangle.Guided ProofShowing Cos x approximation graphically and deriving Tan x approximationCalculating percentage error approximations for cosProve Cos small angle approx.. once double angle identities have been done.How far is the Horizon (nrich)Flight Path (nrich)Problems using radiansSolutions ................
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