9.5 the sine and cosine ratios - wordpress.com · 2018. 4. 9. · a triangle in order to use the...
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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