Transcript Tristan Starck

Topics in
Trigonometry!
BY: ARMAN TAFAZZOLI (5TH)
TRISTAN STARCK (5TH)
BRIAN VICENTE (5TH)
RAY JAY ESPANOLA (4TH)
Trigonometry- definition
 The word trigonometry comes from Ancient
Greek: τρίγωνο" (triangle) + "μετρεῖν" (to
measure).
“Triangle measuring”
 This was it’s given name because
trigonometry had mainly been used for
“triangle measuring” at its time.
History
 There is not much real history about
trigonometry; it’s something that was
discovered and developed over many years.
 Uses of trigonometry date back to times of
Ancient Egypt and Greece
-The Egyptians used a basic form of
trigonometry to build their pyramids. They
wondered that if If a pyramid is 250 cubits high
and the side of its base 360 cubits long, what
would its “seked” be? Seked means the length of
the slope, which would be the hypotenuse. They
used a primitive form of trigonometry for this.
Trig and
the
Pyramids
The Father of Trigonometry, Hipparchus
 Hipparchus- 190 BC- 120 BC
 Hipparchus was a Greek astronomer who was
the first to make accurate models for the
motion of the Sun and Moon that still survive
today.
 His greatest contribution to trigonometry
was constructing the first trigonometric table
 He spent most of his life working on
astronomy. Trig was an outocme of his
astronomy.
Development- the Greeks
 After Hipparchus passed, the Greeks were still
the major power in mathematics.
 Menelaus made theories on spherical
triangles and chords.
 Ptolemy continued on Hipparchus’ work on
chords and made some important formulas
and theorems, the most important being the
half-angle formula.
Hipparchus, the
“Father of
Trigonometry”
Menelaus of Alexandria
Ptolemy
Development- the Islamic World
 The Persians and Arabs converted the early trigonometry
works for the medieval Islamic world.
 The most important contribution to basic trigonometry by
the Muslims:
 Muhammad ibn Mūsā al-Khwārizmī produced accurate sine
and cosine tables, and the first table of tangents. He was
also a pioneer in spherical trigonometry, picking up after
Menelaus of Greece. Besides his enormous contributions to
trig, he is widely known as the creator of algebra.
 In 830, Habash al-Hasib al-Marwazi produced the first table
of cotangents. Muhammad ibn Jābir al-Harrānī al-Battānī
discovered the reciprocal functions of secant and cosecant,
and produced the first table of cosecants for each degree
from 1° to 90°.
Muhammad ibn Mūsā al-Khwārizmī
Habash al-Hasib al-Marwazi
Muhammad ibn Jābir al-Harrānī al-Battānī
Development- Europe
 The biggest contribution to our basic
trigonometry came from Georg Joachim
Rheticus.
 He was the first in Europe to apply
trigonometric functions directly in terms of
right triangles instead of circles, and created
tables for all six trigonometric functions.
Applications of Trig in the Modern World
 The world has used trigonometry and trigonometric
functions in unlimited number of ways. For example,
triangulation is used in astronomy to find the
distance between nearby stars. Also, triangulation is
used to measure distances between major
landmarks. Trigonometry is also used in satellite
navigation systems. Cosine and sine functions are
key to the theory of periodic functions like those that
explains sound and light waves.
Jobs that incorporate trigonometric functions or
trigonometry include almost all sciences, computer
graphics and gaming, pharmacy, number theory,
and electronics.
Diagrams
SOH-CAH-TOA
is a common
tool to
remember the 3
basic trig
functions.
A basic right triangle with angle
theta (Θ)
JUST 4 LAUGHS!