Al-Battani, an Arab astronomer and mathematician from the 9th century, is considered the father of trigonometry. He made significant contributions including developing the first trigonometric tables and correcting the works of Ptolemy. His books, translated into Latin, influenced the development of astronomy in Europe during the Renaissance. The document goes on to discuss determining the values of sine, cosine, and tangent for acute angles without a calculator.

1. C5: TRIGONOMETRIC RATIOS

2. WHAT WILL YOU LEARN?
• SINE
• COSINE
• TANGENT

3. • Al-Battani or Mohammad Ibn Jabir Ibn Sinan Abu Abdullah is the father
of trigonometry.
• He was born in Battan, Damascus. He was an Arabian prince and the
ruler of Syria.
• Al-Battani was recognised as a renowned astronomer and Islamic
mathematician.
• Al-Battani got his early education from his own father Jabir Ibn Sinan
who was a famous scientist of his era. He succeeded in elevating the
level of trigonometry and is the first person to develop the Contangents
Table.
• His works in the field of astronomy were largely influential on Western
academics that it gave rise to the Renaissance era.
• Al-Battani corrected the works of Ptolemy in his book “Al Zaiju al
Sabik”. The book contains a preface and 57 chapters about calculation
methods of constellations, axial tilt of stars and their problems; types of
calendar, time measurement system, astronomical instruments and
their making. The book has been translated into Latin by Plato of Tivoli
and this had had an effect in the development of astronomy in Europe
as can be seen in Copernicus’ research on his finding.
• Among his other works are "Zaiju al Ralqani” which contains his work
“Syarah Arbau'u Maqolat Li Batlimous”, “Kitab Ta' dil Kawakib” and
“Kitab Ma'rifatul Matoli'u al Buruj fima Baina Arba'i al Falak”. He also
had few articles on geography. Al-Battani who was known as the
Ptolemy of Arab or as Albatagnius, had the unusual ability in
succeeding in combining his details of research with the development
of the theory of astronomy

4. 5.1 Sine, Cosine and
Tangent of Acute Angles
in Right-angled Triangles

15. How do you determine the
values of sine, cosine and
tangent of 30°, 45° and
60° angles without using a
calculator?

20. Homework

21. What is the unit of measure for angles?

23. Homework

24. How do you
determine the
values of sine,
cosine and
tangent?

26. Homework

27. How do you calculate the size of an angle by using
trigonometric ratios sine, cosine and tangent ?

29. Homework

30. Problem Solving