High School Mathematics-Physics SMILE Meeting
1997-98 -- 04-05 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 * |_____________*___ DIt follows from trigonometry that
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:
21 March 2006: Fred Schaal (Lane Tech HS,
mathematics)
Graphing Inverse Trig Functions
Fred
noted that books don't tell how to graph inverse trig
functions. Fred figured out a pretty good way to do it with
a TI-83 calculator. He projected the Ti-83 screen on the
wall for us to follow along with his method. He had
written a little program to plot these functions. First
Fred plotted the inverse sin and the plot looked reasonable. But
the same method with the inverse cosine did not give a curve
that made sense. Some adjustments were made in the graph scale, as suggested by the
friendly crowd, and the
inverse cosine curve looked better. Fred then tried the
inverse tangent and it also looked reasonable. Interesting, Fred!
18 April 2006: Porter Johnson (IIT
Physics)
Regular Pentagons and Pentagrams
Porter used the fact that the angles q
= 36^{o} and q =72^{o}
both satisfy the relation sin 5q = 0
to determine the value of cos q for each angle.
He used the basic double angle formulas
You can also use these angles to make a pentagram: http://en.wikipedia.org/wiki/Pentagram. By the way, is it true that pentagrams are always located somewhere on the bodies of werewolves? (See Werewolf: Detection and Prevention: http://www.zerotime.com/night/detect.htm.)