Math Lessons: Trigonometry

High School Mathematics-Physics SMILE Meeting
1997-2006 Academic Years
Mathematics: Trigonometry

27 February 2001 Walter McDonald (CPS Substitute Teacher; VA X-Ray Technician)
showed how to make an indirect measurement of the height H of a building, using trigonometry. He moved a distance D from the building, and measured the angle in the right triangle between the top and bottom, as shown:

                        |
                        | *
                H       |   *
                        |     *
                        |       * 
                        |         *
                        |        q  * 
                        |_____________*___
                                D

It follows from trigonometry that H = D tan q. He illustrated the method by measuring the height of the ceiling, by measuring out D = 16 feet, and then measuring the angle q: [lying flat on the floor to get an accurate reading!] to be q = 30^o. Thus, H = D tan q = 16 feet * tan 30^o = 9.2 feet. Very good, Walter.

Walter McDonald (CPS Substitute and Veterans Administration Diagnostic Radiation Technologist)
showed us this graph of the trigonometric functions [sine, cosine, tangent, cotangent, secant and cosecant] which was obtained from the Microsoft Encarta Encyclopedia.

Walter made the following points:

The sine and cosine are periodic with period 360^o or 2p radians.
The tangent is periodic with periodic with period 180^o or p radians.
The tangent has an asymptote at ± p/2 radians.