Trigonometric Ratios in Right Triangles M. Bruley

Trigonometric Ratios are based on the Concept of Similar Triangles!

All 45º- 45º- 90º Triangles are Similar! 45 º

All 30º- 60º- 90º Triangles are Similar! 1 60º 30º ½ 60º 30º º 30º 1

All 30º- 60º- 90º Triangles are Similar! 10 60º 30º º 30º º 30º

The Tangent Ratio c a b c’ a’ b’ If two triangles are similar, then it is also true that:  The ratio is called the Tangent Ratio for angle   

Naming Sides of Right Triangles   

The Tangent Ratio   Tangent  There are a total of six ratios that can be made with the three sides. Each has a specific name.

The Six Trigonometric Ratios (The SOHCAHTOA model)  

The Six Trigonometric Ratios   The Cosecant, Secant, and Cotangent of  are the Reciprocals of the Sine, Cosine,and Tangent of 

Solving a Problem with the Tangent Ratio 60º 53 ft h = ? We know the angle and the side adjacent to 60º. We want to know the opposite side. Use the tangent ratio: 1 2 Why?

There are three pairs of cofunctions: `The sine and the cosine The secant and the cosecant The tangent and the cotangent Cofunctions p. 287

Acknowledgements  This presentation was made possible by training and equipment provided by an Access to Technology grant from Merced College.  Thank you to Marguerite Smith for the model.  Textbooks consulted were:  Trigonometry Fourth Edition by Larson & Hostetler  Analytic Trigonometry with Applications Seventh Edition by Barnett, Ziegler & Byleen