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)