Trigonometric Functions

Lesia Smith Michael M. Byrne School
5329 S. Oak Park
Chicago IL 60608
(312) 535-2170

Objectives: To define and demonstrate the six trigonometric functions To facilitate using the three most frequently used trigonometric functions Materials Needed: Pythagorean Theorem Model Overhead Overhead Projector Overhead TI81 Graphing Calculator TI81 Graphing Calculator/Individual Spaghetti (12 pieces for each individual) four 3, 4 and 5 cm lengths/each Glue Centimeter Grid/Individual Compass and Protractor Strategy: 1. Discuss the Pythagorean Theorem 2. Demonstrate the Pythagorean Theorem using spaghetti 3. Calculate 6 word problems demonstrating the Pythagorean Theorem 4. Discuss the trigonometric functions 5. Calculate the same 6 word problems demonstrating the trigonometric functions 6. Discuss how the trigonometric table is formed 7. Graph the sine and cosine functions 8. Demonstrate the plotting of sine, cosine and tangent on the graphing calculator 9. Discuss how the answers obtained using the Pythagorean Theorem and the trigonometric functions compare 10. Demonstrate a Real Life Problem by measuring the height of the wall in the room using the tangent function Conclusion: 1. The Pythagorean Theorem gives us the third side of a right triangle when two sides are given. The trigonometric functions give all sides and angles of a right triangle when one side and one of the acute angles are given. It was demonstrated to the class how to find the three sides of a triangle when two sides are given. This was done by using the Pythagorean Theorem and the trigonometric functions. 2. Trigonometry allows calculation of the measures of angles in a triangle when the length of certain sides are known. While we studied right triangles, trigonometry can also be applied to arbitrary triangles. References: Algebra 2 (Prentice Hall Mathematics 1990)
Contemporary's Number Power 3 (The Real World Math, 1988)
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