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# Advanced math/trig - PowerPoint PPT Presentation

Advanced math/trig. Chastity Reynolds. What is trigonometry?. Trigonometry is “the branch of mathematics that deals with the relations between the sides and angles of plane or spherical triangles, and the calculations based on them.” (“Trigonometry”). When/where did trig originate?.

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Chastity Reynolds

• Trigonometry is “the branch of mathematics that deals with the relations between the sides and angles of plane or spherical triangles, and the calculations based on them.” (“Trigonometry”)

• Connected with math and astronomy

• “first work on trigonometric functions related to chords of a circle.” (“The Trigonometric Functions”)

• Originated from a man named Hipparchus

• Greek mathematician

• “The first known table of chords were produced… in about 140 BC.” (“The Trigonometric Functions”)

• Many others followed Hipparchus’s method

• Hipparchus:

• Greek mathematician

• Menelaus: 100 AD

• Rome

• “Producing six books of tables of chords which have been lost but his work on spherics has survived and is the earliest known work on spherical trigonometry.”(“The Trigonometric Functions“)

• Regula sex quantitatum

• Ptolemy

• Influenced by Hipparchus

• “Calculated chords by first inscribing regular polygons of 3,4,5,6, and 10 sides in a circle.” (“The Trigonometric Functions“)

• Used to calculate degrees to find chords

• Hindus:

• In about 500, Aryabhata created sine tables

• Brahmagupta in 628, created sine tables also

• Bhaskara in 1150,showed methods to construct a table of sines for any angle.

• Arabs

• “by 980 Abu’l-Wafa knew..” that sin2x=2 x cos x. (“The Trigonometric Functions“)

• Copernicus, Rheticus, and Regiomontanus also contributed by writing books that were about tables of sines and cosines and “contained work on planar and spherical trigonometry…” (“The Trigonometric Functions“)

• Measuring the floor of a room that is shaped in a circle, to know the measures so that you are able to put down missing carpet.

• “Computers utilize trigonometry to establish the shades and colors of images on a screen.” (“Modern Uses of Trigonometry”)

• “MRI machines scan your body and display the color image on a computer screen.” (“Modern Uses of Trigonometry”)

• “Medical professionals use the results to determine the cause and location of cancers and tumors” (“Modern Uses of Trigonometry”)

• Sine : sin x =

• Cosine: cos x =

• Tangent: tan x =

• Secant: sec x:

• Cosecant: csc x =

• Cotangent: cot x =

• They are related because they use the same ratios ,but the three least used are flipped ratios of the most used ratios.

• Geometry

"Trigonometry Functions - Introduction." Introduction to the 6 Trigonometry Functions. N.p., n.d. Web. 04 Sept. 2012. <http://www.mathopenref.com/trigfunctions.html>.

• "Educational Videos, Lessons and Games for K-12 School Kids." Trigonometry. N.p., n.d. Web. 03 Sept. 2012. <http://www.neok12.com/Trigonometry.htm>.

• Aquatics Bathtub

• Lee Brooks Jr.

• (434) 572 – 1200

• 1100 Industrial Park Rd, South Boston, VA 24592

• Have to measure tub sizes and area to install tubs or other aquatic items.

• The unit circle is a “circle with a radius of one unit in length” "Trigonometry Primer I.“

• Origin center

• Right middle edge

• Counterclockwise

• Triangle within a circle

http://www.processing.org/learning/trig/

• "Trigonometry." Dictionary.com. Dictionary.com, n.d. Web. 31 Aug. 2012. <http://dictionary.reference.com/browse/trigonometry>.

• "The Trigonometric Functions." Trigonometric Functions. N.p., n.d. Web. 31 Aug. 2012. <http://www-history.mcs.st-and.ac.uk/history/HistTopics/Trigonometric_functions.html>.

• Greenberg, Ira. "Trigonometry Primer I." Trig Processing.org. N.p., n.d. Web. 03 Sept. 2012. <http://www.processing.org/learning/trig/>.

• "Educational Videos, Lessons and Games for K-12 School Kids." Trigonometry. N.p., n.d. Web. 03 Sept. 2012. <http://www.neok12.com/Trigonometry.htm>.

• Massey University. "Trigonometry." Trigonometric Ratios, Maths First, Institute of Fundamental Sciences, Massey University. N.p., n.d. Web. 03 Sept. 2012. <http://mathsfirst.massey.ac.nz/Trig/TrigRatio.htm>.

• Turner, Josh. "Modern Uses of Trigonometry." EHow. Demand Media, 05 Apr. 2011. Web. 04 Sept. 2012. <http://www.ehow.com/info_8166929_modern-uses-trigonometry.html>.

• "Trigonometry Functions - Introduction." Introduction to the 6 Trigonometry Functions. N.p., n.d. Web. 04 Sept. 2012. <http://www.mathopenref.com/trigfunctions.html>.