Trigonometric Ratios The term "trigonometry" derives from the Greek (!'thgonometrj'a"), meaning "triangle measuring". Trigonometry specifically deals with the relationships between the sides and the angles of triangles, that is, the trigonometric functions, and with calculations based on these functions. Trigonometry has important applications in many branches of pure mathematics as well as of applied mathematics and, consequently, much of science. Ancient Egj^tians used trigonometry to reset land boundaries after the Nile river flooded each year, and the Babylonians used it to measure distances to nearby stars. Trigonometry is used in engineering, cartography, medical imaging, and many other fields. In this chapter we study the relationship between the ratios of sides of right triangles. These ratios are called Trigonometric Ratios. All Trigonometric functions are used for right triangles only. The three ratios we use in Geometry are SINE, COSINE, & TANGENT. ^•^lEach roMo iS based. .op|x :)sr -[-e TRIGONOMETRIC RATIO Sine of A •„^' Cosine of A Tangent ofA ABBREVIATION Si Cos an DEFINITION _ oppQ^tfe Side I, 6b RATIO PL c b c *** opposite Sidt. ognd 4ne What happens if the angle changes to B? ad^qmlV Sfd^, [1 ^)111^1 S>a5l' -ch/ Can the angle be C? MOj HeVer W|6 -tVie'^O" ATljIe. The right angle is never used in trigonometry, as the hypotenuse doesn't change. A mnemonic to help memorize this JsOHCAHTOAl S-Sine 0-Opposite leg H-Hypotenuse 1 C-Cosine A-Adjacent leg H-Hypotenuse T-Tangent 0-Opposite leg A-Adjacent leg Sni .Y° = Opposite leg Hypotenuse Cos x° = Adjacent leg Hypotenuse Tan .v° = Opposite leg Tan .v° = Adjacent leg