This document discusses trigonometry and its key concepts. It defines trigonometry as a branch of mathematics concerning the study of triangles and the relationship between side lengths and angles. It notes that Hipparchus of Nicaea in the 2nd century BC is considered the father of trigonometry. The document outlines important trigonometric ratios like sine, cosine and tangent, and defines concepts like adjacent, opposite, and hypotenuse sides of a right triangle. It also discusses Pythagoras' theorem relating side lengths in a right triangle.

1. THE SIX
TRIGONOMETRIC
RATIOS
MS. REYBETH D. RACELIS, LPT

2. OBJECTIVES
• Illustrates the six
trigonometric ratios
• Find the trigonometric ratios
of special angles.
• Use trigonometric ratios to
solve problems involving right
triangles.

3. ARITHMETIC
• is concerned mainly with the study
of structure, operations and
applications of whole numbers and
positive rational numbers whether
in the form of fraction, decimal or
percent.

4. ALGEBRA
• is concerned with the study of
the variables represented by
letters and the operations
relating these variables.

5. Advanced Definition of Algebra
Algebra (from Arabic al-jabr meaning
"reunion of broken parts") is the
branch of mathematics concerning the
study of the rules of operations and
relations, and the constructions and
concepts arising from them,
including terms, polynomials,
equations and algebraic structures.

6. FATHER OF ALGEBRA
Muhammad ibn Musa al-Khwarizmi
was a 9th-century Persian Muslim
mathematician and astronomer. He is
known as the "father of algebra", a
word derived from the title of his
book, Kitab al-Jabr.

7. AL-KHWARIZMI, THE FATHER OF ALGEBRA
• Abu Ja'far Muhammad ibn Musa al-Khwarizmi lived in
Baghdad, around 780 to 850 CE (or AD). He was one of
the first to write about algebra (using words, not
letters).
• Around 825 he wrote the book "Hisab Al-jabr w’al-
muqabala", from which we get the
word algebra (meaning 'restoration of broken
parts'). This book included many word problems,
especially dealing with inheritance.
• Al-Khwarizmi helped establish widespread use
of Hindu-Arabic numbers:
• 1, 2, 3, ...

8. • The Hindu-Arabic system was much easier to use when
performing mathematical operations, since it is a
base-10 system. Ever tried to multiply using Roman
numerals...?

9. FATHER OF ALGEBRA
Diophantus of Alexandra
- was a Greek mathematician whom many
have considered as the “Father of
Algebra”. He lived during the 3rd century
A.D. and wrote the treatise Arithmetica.
His fame lies in representing unknown by
“symbols”.

10. GEOMETRY
- is a branch of mathematics that studies
the sizes,shapes,positions angles and
dimensions of things.

11. FATHER OF GEOMETRY
Euclid enters history as one of the
greatest of all mathematicians and he is
often referred to as the father of
geometry. The standard geometry most of
us learned in school is called Euclidian
Geometry.

12. TRIGONOMETRY
• A branch of mathematics that
studies triangles and the
relationship between the
lengths of their sides and the
angles between those sides.

13. • The word trigonometry comes from
the Greek words for triangle
(trigōnon) and measure
(metron).

14. FATHER OF TRIGONOMETRY
Hipparchus of Nicaea
Hipparchus was a Greek astronomer who lived between
190-120 B.C. He is considered the father of
trigonometry, a branch of mathematics which studies
the angles of sides of triangles.

15. CONCEPTS:
• TRIANGLE – a polygon with 3 vertices, 3
sides which are line segments.
• TRIGONOMETRIC RATIO – a ratio that
describes a relationship between a side
and an angle of a triangle

16. • ADJACENT SIDE – the side next to the
reference angle in a right triangle.
• OPPOSITE SIDE – the side across the
reference angle in a right triangle.
• HYPOTENUSE – the longest side of a right
triangle.
- always opposite to the 90°
angle in a right triangle.

17. • RIGHT TRIANGLE – in which one angle
is a right angle.
• SOH-CAH-TOA – a mnemonic used for
remembering the equation.
• MNEMONIC – a tool used to help
remember fact or large amount of
information.

18. Sine, Cosine and Tangent
The main functions in trigonometry are Sine, Cosine
and Tangent
They are simply one side of a right-angled triangle
divided by another.
For any angle "θ":
(Sine, Cosine and
Tangent are
often abbreviated
to sin, cos and tan.)

19. OTHER FUNCTIONS (COTANGENT, SECANT,
COSECANT)
Similar to Sine, Cosine and Tangent, there are
three other trigonometric functions which are
made by dividing one side by another:

20. PYTHAGOREAN THEOREM
• states that the square of the
hypotenuse of a right triangle
is equal to the sum of the
squares of the other two sides.
c² = a² + b²

21. •Pythagoras of Samos is
often referred to as the first
pure mathematician. Greek
philosopher, mathematician, and
discovered the Pythagorean
theorem.

22. EXERCISES
13
5
12