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Trigonometry

Jaden Nichols. Trigonometry. What is Trigonometry?. the first part of the word is from Greek trigon "triangle". The second part of trigonometry is from Greek metron "a measure.“ The Indo-European root is me- "to measure.“

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Trigonometry

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  1. Jaden Nichols Trigonometry

  2. What is Trigonometry? • the first part of the word is from Greek trigon "triangle". • The second part of trigonometry is from Greek metron "a measure.“ • The Indo-European root is me- "to measure.“ • Trigonometry is literally the measuring (of angles and sides) of triangles. • Trigonometry defines relations between elements of a triangle. • It is a branch of geometry. http://www.cut-the-knot.org/WhatIs/WhatIsTrigonometry.shtml

  3. When & Where did it Originate? • It came from Ancient Egyptian and Babylonian times as a way to work with triangles. • Trigonometry emerged as a way to work with triangles and circles in the 15th century. http://www.cut-the-knot.org/WhatIs/WhatIsTrigonometry.shtml

  4. Discovery? • It took more than one mathematician to discover trigonometry. • Hipparchus-trig table that measured length for angles • Ptolemy-table increasing chords by 1 degree • Indian mathematicians-sine functions rather than chords • Muslim astronomers-studies by the Greeks and Indians http://www.trigonometry-help.net/history-of-trigonometry.php

  5. Trigonometry in the Real World • Civil Engineering-calculating surfaces and shapes • Sailors-navigation, determining position • Astronomy-the locations and shapes of the planets • Electronic fields-quick calculating with math and science • Carpenters-building, shaping

  6. Functions • 3 most used functions and their ratios: • Sine=opposite/hypotenuse • Cosine=adjacent/hypotenuse • Tangent=opposite/adjacent • Other 3 functions and their ratios: • Cosecant=hypotenuse/opposite • Secant=hypotenuse/adjacent • Cotangent=adjacent/opposite • Yes, they are related. • Reciprocal functions!

  7. Functions http://www.regentsprep.org/Regents/math/algtrig/ATT1/trigsix.htm

  8. Interesting Website • http://www.regentsprep.org/Regents/math/algtrig/ATT1/trigsix.htm • This was the best website I found. It shows the functions and their ratios. It also shows their relations and other things. It isn’t plain looking and it was kid-friendly!

  9. Unit Circle • A circle with a radius of 1 with its center at 0. • Because the radius is 1, it is easy to measure sine, cosine, and tangent.

  10. Unit Circle

  11. Triangles & Circles • They are related. • They are used in trig, can be measured in similar ways.

  12. Project Idea • Scoring a goal in soccer is done with a variety of different shot positions, but each position involves knowing the length and depth of the goal. The distance from the goal, diameter of the soccer ball and height of the goal form a variety of angles demonstrating triangular scoring patterns in soccer.

  13. Project Idea • We could study and make a chart or graph about the different angles and shot positions. http://www.ehow.com/list_5939810_high-school-trigonometry-project-ideas.html

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