Alicia Stith

What is Trigonometry?  A type of math with a connection with angles, sides of triangles, and functions of angles

Origins of Trigonometry  Comes from the word “sine”  “Sine” uncovers trigonometry’s roots in Babylonian, Greek, Hellenistic, Indian, and Arabic mathematics and astronomy

Mathematicians  Hipparchus -produced the first known table of chords in 140 BC  Menelaus and Ptolemy continued Hipparchus’ work

Applications of Trig.  Optics and statics – helps understand space  military engineers – help build things in the military  Navigation- used on voyages ex: Columbus carried a copy of Regiomontanus' Ephemerides Astronomicae on his trips to the New World

Trig. Functions  Most Used: Sine (sin), Cosine (cos), Tangent (tan)  Other 3: Secant (sec), Cosecant (csc), Cotangent (cot)  The six trig. Functions are related b/c all involve using the opposite, hypotenuse, adjacent  I’ve seen these functions in Algebra II before this research 

Trig. Websites  

Trig. Project  Sports  A variety of sports involve angles that double as motions and patterns when executing plays. For example, 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. A bowler uses trigonometry to figure out where to throw the ball, at what point the ball will curve and the distance the ball is thrown on the lane in order to score. A project centered around those concepts and various spare shots, for example, demonstrates various angular properties. Football players use trigonometry when tackling a player. A student interested in this concept could attend a football practice and create a project about the best tackling angles.

Unit Circle  Circle with a radius of one  used to recognize the sines, cosines, and tangents of angles in a circle  points on the circle creates an angle with the positive x-axis when a line is drawn from the point to the origin; x-coordinate of that point is the cosine of the angle; sine of the angle is the y-coordinate of the point.