Trigonometry Project
Trigonometry Project BY: JERRY STIEG What is Trigonometry? The word trigonometry comes from Greek words meaning “the measurement of triangles” It is “the study of angles and of the angular relationships of planar and three-dimensional figures” (Weisstein) Weisstein, Eric W. "Trigonometry." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Trigonometry.html When/Where did Trigonometry originate? Trigonometry is thought to have originated in Greece, with ideas from Arabia and India It was created by astronomers and mathematicians trying to calculate the distance of surrounding stars and planets Origins do not necessarily lie with plane triangles. How Many Mathematicians Were Responsible? Trigonometry is not something that was simply stumbled upon It took many years and different minds to advance it. Hipparchus- Greek Mathematician- Gave a method for solving spherical triangles Menelaus- Also a Greek Mathematician- Expanded on Hipparchus’s ideas and developed “Menelaus’s Theorem” Ptolemy- “relied on Babylonian observations and traditions”(Smoller)- one of the most influential Mathematicians of his time. Smoller, Laura. "The Birth of Trigonometry." The Birth of Trigonometry. UALR, May 2001. Web. 30 Aug. 2012. <http://ualr.edu/lasmoller/trig.html>. How Many Mathematicians Were Responsible? Hipparchus Ptolemy Examples of Trigonometry In order to fly over a mountain, you must know how tall the mountain is. Trigonometry can be used to calculate how tall a mountain is so that today’s airplanes can fly over them at a safe elevation. In order to calculate this you would place yourself a certain distance away from the mountain and then measure the angle to the top of the mountain. You then would use the tangent Trig function. This would allow you to calculate the height of the mountain which is opposite of the angle you know and adjacent to the distance you know. In much the same way, astronomers use Trig to calculate the distance of stars and other objects in astronomy. By knowing the distance to the moon astronomers can use it to calculate to position of most extraterrestrial objects. Sound engineers often use Trig because a computer does not usually recognize sounds like a human, but in a mathematical way. They often use the sine and cosine functions to calculate the sound waves. Trigonometry is also used in architecture. It takes the guessing out of construction by allowing builders to calculate side with the information given to them. What Are the Three Most Common Trig Functions? The three most popular There are three other less Trig functions are: Sine (sin): common trig functions: Cosecant Function (csc): Opposite/Hypotenuse Cosine (cos): Adjacent/Hypotenuse Tangent (tan): Opposite/Adjacent Hypotenuse/Opposite Secant Function (sec): Hypotenuse/Adjacent Cotangent Function (cot): Adjacent/Opposite Are These Six Functions Related? The extra three are simply the reciprocals of the original three functions. The only place I have ever seen these functions outside of this research was is geometry class when we were studying triangles. What is a Unit Circle? “A unit circle is a circle where the radius is 1 (one unit). The unit circle equation is x² + y² = 1” This is used in cooperation with triangles by dividing it into pieces. It is helpful in figuring out functions Bee, Johnathan. "Unit Circle Trigonometry." Unit Circle Trigonometry. N.p., n.d. Web. 31 Aug. 2012. <http://www.snow.edu/jonathanb/Courses/Math1060/unit_ci rc_trig.html> Trigonometric Career Example I often use a basic form of Trigonometry myself in my job as a woodsman. Since we use a select cut technique, we have to pick and choose what trees we fall I do this by using a Biltmore stick. This stick is to be used by stepping sixty-six feet away from a tree and using the stick as a visual reference to how many 16 foot logs can be cut from the tree, without actually putting the tree on the ground. This is much like measuring the mountains in my former examples. The product of this work is to allow me to know how many board feet are in a log and whether it is worth the time to cut it. Link http://www.youtube.com/watch?v=t2uPYYLH4Zo is an informative, but extremely goofy video. It covers the basics of what I remember of Trigonometry from Geometry class. Works Cited Bee, Johnathan. "Unit Circle Trigonometry." Unit Circle Trigonometry. N.p., n.d. Web. 31 Aug. 2012. <http://www.snow.edu/jonathanb/Courses/Math1060/unit_circ_trig.html>. Hayes, Malcolm E. "Welcome to Trigonometry." Welcome to Trigonometry. University of Missouri, 2002. Web. 30 Aug. 2012. <http://braintrax.mst.edu/math/trig/trig_content/trigwelcome.htm>. Pierce, Brandon. "What Are Some Applications of Trigonometry?" EHow. Demand Media, 10 Aug. 2011. Web. 31 Aug. 2012. <http://www.ehow.com/info_10052141_applications-trigonometry.html>. Roberts, Donna. "The Six Trigonometric Functions and Reciprocals." The Six Trigonometric Functions and Reciprocals. Oswego City School District Regents Exam Prep Center, 2012. Web. 31 Aug. 2012. <http://www.regentsprep.org/Regents/math/algtrig/ATT1/trigsix.htm>. Smoller, Laura. "The Birth of Trigonometry." The Birth of Trigonometry. UALR, May 2001. Web. 30 Aug. 2012. <http://ualr.edu/lasmoller/trig.html>. Weisstein, Eric W. "Trigonometry." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Trigonometry.html
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