9.5TheSineandCosineRatiosSineandCosineareverysimilartothatofTangent,exceptforoneimportantdifference.WhileTangentinvolvesthelengthsofbothlegsofarighttriangle,SineandCosinearetrigonometricratiosforacuteanglesthatinvolvethelengthsofalegandthehypotenuseofarighttriangle.Example1:FindingSineandCosineRatiosFindsin $ , sin & , cos $ , cos &.Writeeachanswerasafractionandasadecimalroundedtofourplaces.Doyouseeanypatterns?Example2:RewritingTrigonometricExpressionsWritesin 56+intermsofcosine

Example3:FindingLegLengthsFindthevaluesofxandyusingsineandcosine.Roundyouranswertothenearesttenth`Tryonyourown:

1) Writecos 23+intermsofsine.

2) Findthevaluesofuandtusingsineandcosine.AngleofDepression:TheanglethatadownwardlineofsightmakeswithahorizontallineExample4:ModelingwithMathematicsYouareskiingonamountainwithanaltitudeof1200ft.Theangleofdepressionis21o.Findthedistanceyouskidownthemountaintothenearestfoot.Homework:4,6,9-21odd,26*,27,30,36,41-44