TRIG

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WHAT IS TRIGONOMETRY?

• “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?

• Dates back to early ages of Egypt and Babylon

IS ONE MATHMATICIAN RESPONSIBLE FOR ITS DISCOVERY OR MORE THAN ONE?• History of trigonometry was advanced by the Greek

astronemer Hipparchus

• 5th century: Ptolemy created table of chords with increasing 1 degree.

• Indian mathematicians created the trig system based on sine function instead of chords.

• 13th century: Germans modern trig by defining trig functions as ratios rather than lengths of lines.

4 REAL WORLD APPLICATIONS THAT INVOLVE TRIGONOMETRY• “A church tower stands 35 metres high, its shadow is

measured at 50 metres. Find the angle of elevation of the sun “(Trigonometry(i))

• “A plane is flying at 10,000 metres altitude directly above, 12 seconds later the angle of elevation is 75, find the speed of the plane”(Trigonometry(i))

• “You are standing 20 feet away from a tree, and you measure the angle of elevation to be 38°. How tall is the tree?”(High)

• “You are standing on top of a building, looking at park in the distance. The angle of depression is 53°. If the building you are standing on is 100 feet tall, how far away is the park? Does your height matter?” (High)

TRIGONOMETRY FUNCTIONS

• What are the 3 most used trig functions and their ratios?• Sine : opp/hyp• Cosine :adj/hyp• Tangent :opp/adj

• What are the other 3?• Cosecant :hyp/opp• Secant :hyp/adj• Cotangent :adj/opp

• How are these functions related?• They have to deal with right angle triangles. The other 3 deal with

inverted fractions.

• We have seen this before in Geometry class

INTERESTING WEBSITE LINK

http://www.purposegames.com/games/?t=1671&so=mp

It has a lot of interesting games and practices.

TRIGONOMETRY PROJECT IDEA

Make a sextant “Make a sextant from a protractor and a piece of string about a foot

long. Tie one end of the string to the hole in the center of the protractor. When the bottom of the protractor is on the ground and the string points to the top of an object, hold the string against the protractor and read off the angle of elevation. Hold the protractor sideways to read off the angle to the ends of objects like bridges”(Mano)

WHAT IS THE UNIT CIRCLE?

A circle where the radius in 1 unit

Why and how is it used in trigonometry? To define the sine, cosine, and tangent functions

WORKS CITED

"Basic Trigonometric Ratios." Purplemath.com. N.p., n.d. Web. 4 Sept. 2012. <http://www.purplemath.com/modules/basirati.htm>.

"History of Trigonometry." History of Trigonometry. N.p., n.d. Web. 04 Sept. 2012. <http://www.trigonometry-help.net/history-of-trigonometry.php>.

"High School Trigonometry/Applications of Right Triangle Trigonometry." - Wikibooks, Open Books for an Open World. N.p., n.d. Web. 04 Sept. 2012. <http://en.wikibooks.org/wiki/High_School_Trigonometry/Applications_of_Right_Triangle_Trigonometry>.

"Trigonometry." Dictionary.com. Dictionary.com, n.d. Web. 04 Sept. 2012. <http://dictionary.reference.com/browse/trigonometry>.

"Trigonometry(i)." Trigonometry(i). N.p., n.d. Web. 04 Sept. 2012. http://www.ict-teacher.com/Mathstutor/Trigonometry(i).html.

WORKS CITED

Mano, Carlos. "Ideas for Trig Projects." EHow. Demand Media, 01 July 2011. Web. 04 Sept. 2012. <http://www.ehow.com/info_8674543_ideas-trig-projects.html>.

"Trigonometry Facts: The Amazing Unit Circle." Trigonometry Facts: The Amazing Unit Circle. N.p., n.d. Web. 04 Sept. 2012. <http://mathmistakes.info/facts/TrigFacts/learn/uc/uc.html>.