- By
**ganit** - Follow User

- 173 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' Advanced math/trig' - ganit

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

### 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?

- 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

Mathematicians who discovered trig. Menelaus: 100 AD Ptolemy

- Hipparchus:
- Greek mathematician

- 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

- 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

Mathematicians who discovered trig. Arabs

- 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.

- “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“)

Real-world applications/scenarios that involve trig.

- 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”)

Trigonometric functions

- 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>.

Interesting website about 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>.

Jobs that use trigonometry

- 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.

What is the Unit circle?

- 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/

Works cited

- "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>.

Download Presentation

Connecting to Server..