IB›IB Maths: Analysis and Approaches HL›Mind maps3.2 Right-angled and non-right-angled trigonometryIB Maths: Analysis and Approaches HL: 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=adjoppAngle: use sin−1\sin^{-1}sin−1, cos−1\cos^{-1}cos−1, tan−1\tan^{-1}tan−1Re-label sides for each angleSine ruleasinA=bsinB=csinC\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}sinAa=sinBb=sinCcNeeds a side and its opposite angleAngle form: sinAa=sinBb\frac{\sin A}{a}=\frac{\sin B}{b}asinA=bsinBFind the third angle firstCosine rulec2=a2+b2−2abcosCc^2=a^2+b^2-2ab\cos Cc2=a2+b2−2abcosCTwo sides and included angle: find 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 obtuseTrigonometryany trianglesincostanTriangle areaArea =12absinC=\frac12ab\sin C=21absinCCCC is between sides aaa and bbbPQ=8PQ=8PQ=8, PR=5PR=5PR=5, P=60∘P=60^\circP=60∘: 10310\sqrt3103A median halves the areaChoosing a toolRight angle: SOH CAH TOASide and opposite angle: sine ruleIncluded angle or three sides: cosine ruleLargest side faces the largest angleExam tipsEvaluate 2abcosC2ab\cos C2abcosC as one termWrong side on left of the cosine ruleKeep full values; round only at the end3 s.f. lengths, 1 d.p. angles