IB›IB Maths: Analysis and Approaches SL›Mind maps3.2 Right-angled and non-right-angled trigonometryIB Maths: Analysis and Approaches SL: Mind mapStudy pack PDFAlso for this subtopic:Revision notesFlashcardsSubtopic testCover factsRight-angledsinθ=opphyp\sin\theta = \frac{\text{opp}}{\text{hyp}}sinθ=hypoppcosθ=adjhyp\cos\theta = \frac{\text{adj}}{\text{hyp}}cosθ=hypadjtanθ=oppadj\tan\theta = \frac{\text{opp}}{\text{adj}}tanθ=adjoppPythagoras for a missing sideInverse functions find an angleSine ruleasinA=bsinB=csinC\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}sinAa=sinBb=sinCcNeed a side and its opposite angleFind angles with sinAa=sinBb\frac{\sin A}{a} = \frac{\sin B}{b}asinA=bsinBFind the third angle first: sum is 180∘180^\circ180∘Cosine rulec2=a2+b2−2abcosCc^2 = a^2 + b^2 - 2ab\cos Cc2=a2+b2−2abcosCTwo sides and included angle → third sideThree sides: cosC=a2+b2−c22ab\cos C = \frac{a^2+b^2-c^2}{2ab}cosC=2aba2+b2−c2cosC<0\cos C < 0cosC<0 means obtuseTrigonometrytriangles and rulessincostanAreaArea=12absinC\text{Area} = \frac{1}{2}ab\sin CArea=21absinCCCC is between sides aaa and bbb8,5,60∘8, 5, 60^\circ8,5,60∘ gives 10310\sqrt{3}103A median halves the areaChoosing a toolRight angle: SOH CAH TOASide and opposite angle: sine ruleTwo sides and included angle: cosine ruleKeep full values, round at the endExam tipsRe-label opp and adj for each new angleEvaluate 2abcosC2ab\cos C2abcosC as one termCosine rule: left side is opposite the angleLargest side faces the largest angle