ib maths radians, arc length & sector area

• 1. CIRCULARMEASURE ARCLENGTHSECTORAREA Bytheendofthelessonyoushouldbeableto: 1.Convertdegreesintoradiansandviceversa. 2.Recognizepartsofacircleanduseappropriateterminology. 3.Usepriorknowledgeonlengthofcircumferenceandareaofcircleto deduceformulaetocalculatearclengthandsectorarea. 4.Usepriorknowledgeonthetrigonometricformulafortheareaofa triangletodeduceawaytocalculatetheareaofasegment. 5.Solveproblemsinvolvingarclength,sectorareaandareaofa segment.

2. The unit circle 3. 2rad=360o rad=.... rad=...... .......rad=270o 4. Expressinradians 45o 60o 30o Toconvertdegreestoradians,multiplyby 5. Toconvertradianstodegrees,multiplyby Expressindegrees: 6. Fillintheblanksinthefollowingtable 7. Oneradianisdefinedasthesizeofangle correspondingtoanarcoflength1unitina circleofradius1unit. 1unit =1radian 8. diameter A B O C D E O P Q radius minorsector chord minorsegment majorarc 9. CalculatethelengthoftheminorarcAB: A B Arclength=2 rx 360 Arclength=2 rx 2 in degrees: in radians: Arclength =r 10. CalculatetheareaoftheminorsectorAOB: A B in degrees: in radians: SectorArea =r2 Sectorarea= r2 x 360 Sectorarea= r2 x 2 11. Reminder: A B C a b c Areaoftriangle=xproductanytwosidesxsin(includedangle) Areaofatriangle Areaoftriangle=absinC 12. 30 22 12cm 5cm Calculate the area of the triangle: Areatriangle=15cm2 13. How can we calculate the area of the minor segment? Areasegment=AreasectorAOBAreatriangleAOB Areasegment= Areasegment= A O B 14. How can we calculate the area of the major segment? Areasegment=AreasectorAOB+AreatriangleAOB Areasegment= Areasegment= A O B 15. Atendoflesson... TerminologyQuiz Seenextpage... 16. 1)Thedistancearoundtheedgeofacircle. Circumference 2)Thecircumferenceofanycircledividedbyitsdiameter. Pi 3)Aportionofthecircumferenceofacircle. Arc 4)Astraightlinethatlinkstwopointsonacircumference. Chord 5)Alinefromthecenterofacircletoapointonthecircle. Radius 6)Giventwopointsonacircumference,theshortestarclinkingthem. Minorarc 7)Thedistancealongthecurvedlinemakingupthearc. Arclength 8)Theareaenclosedbytworadiiofacircleandtheirinterceptedarc. Apieshapedpartofacircle. Sector 9)Theregionbetweenachordofacircleanditsassociatedarc. Segment 17. Attachments ArclengthandSectorareaPastpapersProblems.rtf