• Trigonometry is derived from Greek words trigonon(three angles) and metron (measure).• Trigonometry is the branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of the triangle is 900.

• Trigonometry specifically deals with relationships between the sides and the angles of a triangle, i.e. on the trigonometric functions, and with calculations based on these functions.

Trigonometry

History• The origins of trigonometry can be traced to the ci-vilizations

of ancient Egypt, Mesopotamia and the

Indus Valley, more than 4000 years ago.

• Some experts believe that trigonometry

was originally invented to calculate

sundials.

• The first recorded use of trigonometry

came from the Hellinistic mathematician

Circa in 150 BC.

• Many mathemiticians like Aryabhatta, Ibn Yunus

and Al-Kashi also contributed significantly.

Right Triangle

• A triangle in which one angle is equal to 900 is called a right angled triangle.

• The side opposite to the right angle is known as hypotenuse.

AC is the hypotenuse

• The other two sides are known as legs or base and altitude

AB and AC are base and altitude respectively

Pythagoras Theorem

• In any right triangle, the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares whose sides are the two legs.

• In the figure, AC2 = AB2 + BC2

Trigonometric Ratios

Sine (sin) Opposite side / Hypotenuse

Cosine (cos) Adjacent side / Hypotenuse

Tangent (tan) Opposite side / Adjacent side

Cosecant (cosec) Hypotenuse / Opposite side

Secant (sec) Hypotenuse / Adjacent side

Cotangent (cot) Adjacent side / Opposite side

Value for Trigonometric Functions for Angle C

• Sinθ = AB/AC

• Cosθ = BC/AC

• Tanθ = AB/BC

• Cosecθ = AC/AB

• Secθ = AC/BC

• Cotθ = AC/AB

Value of Trigonometric Functions

Trigonometric Identities

Some Applications of Trigonometry

• Main use is in Construction or else this field of mathematics can be applied in astronomy,navigation, acoustics medical imaging, civil engineering, seismology, electrical engineering phonetics, chemistry, number theory and many more.

Real life Applications of Trigonometry

Conclusion

• Trigonometry is a branch of Mathematics with several important and useful applications.

Hence, it attracts more and more research with several theories published year after year.

Thank you!