CIRCULAR MEASURE ARC LENGTH SECTOR AREA By the end of the lesson you should be able to: 1. Convert degrees into radians and viceversa. 2. Recognize parts of a circle and use appropriate terminology. 3. Use prior knowledge on length of circumference and area of circle to deduce formulae to calculate arc length and sector area. 4. Use prior knowledge on the trigonometric formula for the area of a triangle to deduce a way to calculate the area of a segment. 5. Solve problems involving arc length, sector area and area of a segment.
IB Maths Radians, arc length & sector area
May 25, 2015
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- 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
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