Trigonometric functions - Mathcentre

Wetakeacirclediagramsimilartotheoneweusedforthesinefunction. Butnowwelookatthehorizontalaxiscoordinateofthepointwherethelineandthecirclemeet,tofindthevalueof cos x.Theinformationfromthispicturecanalsobeusedtoseehowchanging xaffectsthevalueofcosx. Wecanuseatableofvaluestoplotselectedpointsbetween x = 0 ◦ and x = 360 ◦ ,anddrawasmoothcurvebetweenthem.Wecanthenextendthegraphtotherightandtotheleft,becauseweknowthatthegraphrepeatsitself.x 0 ◦ 45 ◦ 90 ◦ 135 ◦ 180 ◦ 225 ◦ 270 ◦ 315 ◦ 360 ◦cosx 1 0.71 0 −0.71 −1 −0.71 0 0.71 1f(x)1f(x) = cos x−360°360° 720°x0−1Againyoucanseethat cosxmustliebetween −1and1.Thisfunctionalsohasperiodicity 360 ◦ ,or 2πifweworkinradians.Aswith sin x,weshouldliketodefineaninversefunctiontotellustheanglehavingacosineof,say, 1 2 .Unlesswerestrictthedomainof cosx,therewillbemanyanglesthatcouldbe cos−1 1 2 .Whenwedefinedtheinversesinefunction,werestrictedthedomainof sin xto −90 ◦ ≤ x ≤ 90 ◦ .Letusseewhathappensifwedothisfor cos x.f(x)1f(x) = cos x12x−90°90°0−1c○mathcentreJune25,2009 www.mathcentre.ac.uk 6 mc-TY-trig-2009-1