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9.5 Trigonometric Ratios Sin-Cos-Tan What is Trigonometry? • Trigonometry (from Greek trigōnon "triangle" + metron "measure") is a branch of mathematics that studies triangles and the ratios between their sides and the angles between these sides. The field evolved during the third century BC as a branch of geometry used extensively for astronomical studies. It is also the foundation of the practical art of surveying. http://en.wikipedia.org/wiki/Trigonometry Right Angle Trigonometry The Ratio used in Right Angle Trigonometry are Sine – Sin c Cosine – Cos a Tangent - Tan b Right Angle Trigonometry The Ratio used in Right Angle Trigonometry a Sin A c b Cos A c a Tan A b c a b Right Angle Trigonometry The Ratio used in Right Angle Trigonometry opposite SinA hypotenuse adjacent CosA hypotenuse opposite TanA adjacent c a b Right Angle Trigonometry The Ratio used in Right Angle Trigonometry opposite SinA SOH hypotenuse adjacent CosA CAH hypotenuse opposite TanA TOA adjacent c a b How to Remember the Ratio Chief SOH – CAH - TOA opposite SinA SOH hypotenuse adjacent CosA CAH hypotenuse opposite TanA TOA adjacent Right Angle Trigonometry The Ratio used in Right Angle Trigonometry B 5 Sin A .3846 13 12 Cos A .9231 13 5 Tan A .4167 12 13 A 12 5 C Right Angle Trigonometry The Ratio used in Right Angle Trigonometry B 2.5 Sin A .3846 6.5 6 Cos A .9231 6.5 2.5 Tan A .4167 6 13 5 6.5 A 2.5 6 12 C