This document provides an overview of trigonometry and trigonometric ratios. It discusses: 1) Hipparchus, an ancient Greek astronomer, was one of the first to use trigonometry. 2) The basic parts of a right triangle are defined as the hypotenuse, perpendicular, and base. 3) There are six trigonometric ratios that relate the sides of a right triangle - sine, cosine, tangent, cotangent, cosecant, and secant. These ratios use the angles and sides of the triangle.

1. Trigonometry ™ Arjit Saraswat Submitted by :- ® Hipparcus – 190 BC to 120 BC – born in Nicaea (now Turkey) was a Greek astronomer who is considered to be one of the first to use trigonometry.

2. Aryabhatta Indian Mathematician Parts of a Right Triangle B Hypotenuse Perpendicular A C Base Now, imagine that you move from angle A to angle B still facing into the triangle. Imagine that you, the happy face, are standing at angle A facing into the triangle. You would be facing the perpendicular side You would be facing the perpendicular side and standing next to the base. and standing next to the base. The hypotenuse is neither opposite nor adjacent.

3. Review Pythagorus Samian Mathematician B For Angle A Hypotenuse This is the Perpendicular Perpendicular Perpendicular This is the Base A Base Base B For Angle B This is the Perpendicular Hypotenuse This is the Base A

4. Trig Ratios Ramanujam Indian Mathematician B Using Angle A to name the sides Hypotenuse Use Angle B to name the sides Perpendicular We can use the lengths of the sides of a right triangle to form ratios. There are 6 different ratios that we can make. A Base The ratios are still the same as before!!

6. The names also refer to an anglePerpendicular A Base Sine of Angle A = Cosecant of Angle A = Cosine of Angle A = Secant of Angle A = Cotangent of Angle A = Tangent of Angle A =

7. Trig Ratios Freitag German Mathematician B Hypotenuse If the angle changes from A to B Perpendicular The way the ratios are made is the same Base Sine of Angle = Cosecant of Angle = B B Cosine of Angle = B Secant of Angle = B B Cotangent of Angle = Tangent of Angle = B

9. SPHCBHTPB Quetelet Flemish Mathematician B Hypotenuse Here is a way to remember how to make the 3 basic Trig Ratios Perpendicular A Base 1) Identify the Perpendicular side and Base for the appropriate angle Remember “SPHCBHTPB” and it means :- Some People Have Curly Beautiful Hair To Preserve Beauty Use the underlined letters to make the word SPH-CBH-TPB

10. Lame French Mathematician Example B First we will find the Sine, Cosine and Tangent ratios for Angle A. 10 6 Perpendicular A Next we will find the Sine, Cosine, and Tangent ratios for Angle B 8 Base Remember SPH-CBH-TPB Cosec B = Sin A = Sec B = Cos A = Cot B = Tan A =

11. Alberti Italian Mathematician Trigonometric ratios

12. Created By :- Trigonometry Arjit Saraswat Class : X B School : GMSSS-35,Chd Trigonometry ©2010 Saraswat Bros. Ltd.