Topics in Trigonometry!

# Topics in Trigonometry!

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## Topics in Trigonometry!

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1. Topics in Trigonometry! By: ArmanTafazzoli (5th) Tristan Starck (5th) Brian vicente (5th) Ray Jay Espanola (4th)

2. 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.

3. 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.

4. Trig and the Pyramids

5. 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.

6. 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.

7. Hipparchus, the “Father of Trigonometry” Menelaus of Alexandria Ptolemy

8. 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 ibnMūsā al-Khwārizmīproduced accurate sine and cosine tables, and the first table of tangents. He was also a pioneer inspherical 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 ibnJābir 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°.