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angles p2 - Maths Study Sheet 1 7 a n g I e s measuring...

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Unformatted text preview: Maths Study Sheet 1 7 a n g I e s measuring angles part 2 — This UNIT eensists ef 2 parts. Part 2 deals with radians as a unit fer measuring angles. flbjeetives When yen have werked threugh Part 2, yeu sheuld be able te I define radian measure fer an angle - ehange an angle measured in degrees inte radian measure. and Viee—versa ' be familiar with serne ef the eemmenljr—used angles expressed in radians. PIE-requisites: Angles measured in degrees {See Part 1]. The number n (appresimately equal te 3.142}. The eireumferenee ef a eirele ef radius r has a length Zarr . IHtrOdUCthn In Part 1 angles were measured in degrees. If yen wish te stud},r ealeulus er selve equatiens whieh ir‘welve sine, eesine er tangent tunetiens. yeu will need te use anether unit ef rnea surernent fer angles. This is radian measure. Radians are defined in the eentest ef eireles and se this system is alse knewn as eireular measure. Definitien An angle sf 1 radian measure supperts an are ef a trirele whieh is equal in length tn the radius ef the eirele. If the circle has radius r the length et are is r units. we write 1 radian as 1“ [e standing fer circular) Connection Similarly, an angle ef 2 radians supper-ts an are ef length 2r units. between degrees This ean be feimd by remembering twe facts and radians I the length ef the eireumferenre ef a circle is 211? , i the angle at the eenlre which supperts a eemplete eirele is 360” angle. Cemparing the equal ratins, are AB in the whale eirenrnferenee, and angle. AIDS in the angle 360“ we have C r _ 1 Ear 36H” if: 1 1f.' 2a? b 3500 r units B Multiplying by 2:? and 360'” en beth sides, this becomes 360’“: — 'T'ir‘ In wards, a eempleie turn eensisfs ef 2a? radians. Dividing by 2 we ebtain the key equatien eenneeting degrees and radians. 130“: a" Other eenneetinns freqHEntly used are 9G“: g radians 45'”: g radians eU”=-:~ radians 3DD= g radians Exercise Solutions Example 1 Change ?5“‘ Late radian measure. If 180‘”: at . . i. then 1r: EEG Fr :3 se 3'5‘”: [75 rs: —] 130 ‘3 '5 simplifying this T5”: If] Example 2 4 _ Change --3- .fi': radians mre degree measure. Since 180“; a" 4 _ 4 ‘: then —:=<: 130”: [ a] 3 .3 . L. se 240”: e) rs.) 1. Hnw many radians de the fellewmg angles measure? {a} 1 see (b) ere (e) 135* {:1} 300a. Change these angles re degree measure {1 E (by 3m (3 5:: (d) “n: a _ _ 1 a __ 12 2 L e 9 2 rr 3 ‘3 u} —a b n e —e d —a 3 ( ) 9 i i 4 IE ) ,5 (.1) 15s (b) 2res {e} 1500 (d) 220” ...
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angles p2 - Maths Study Sheet 1 7 a n g I e s measuring...

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