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9.5 The Sine and Cosine Ratios Sine and Cosine are very similar to that of Tangent, except for one important difference. While Tangent involves the lengths of both legs of a right triangle, Sine and Cosine are trigonometric ratios for acute angles that involve the lengths of a leg and the hypotenuse of a right triangle. Example 1: Finding Sine and Cosine Ratios Find sin $ , sin & , cos $ , cos &. Write each answer as a fraction and as a decimal rounded to four places. Do you see any patterns? Example 2: Rewriting Trigonometric Expressions Write sin 56 + in terms of cosine

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Page 1: 9.5 The Sine and Cosine Ratios - WordPress.com · 2018. 4. 9. · a triangle in order to use the sine ratio and what you must know about a triangle in order to use the cosine ratio

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

Page 2: 9.5 The Sine and Cosine Ratios - WordPress.com · 2018. 4. 9. · a triangle in order to use the sine ratio and what you must know about a triangle in order to use the cosine ratio

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

Page 3: 9.5 The Sine and Cosine Ratios - WordPress.com · 2018. 4. 9. · a triangle in order to use the sine ratio and what you must know about a triangle in order to use the cosine ratio
Page 4: 9.5 The Sine and Cosine Ratios - WordPress.com · 2018. 4. 9. · a triangle in order to use the sine ratio and what you must know about a triangle in order to use the cosine ratio
Page 5: 9.5 The Sine and Cosine Ratios - WordPress.com · 2018. 4. 9. · a triangle in order to use the sine ratio and what you must know about a triangle in order to use the cosine ratio

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3.2 The Sine and Cosine Ratios - Weeblycolafson.weebly.com/.../3.2_the_sine_and_cosine_ratios.pdf · 2018. 9. 6. · 3.2 Sine and Cosine Ratios 3.2 The Sine and Cosine Ratios Ch 3

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