Trigonometry deals with relationships between the sides and angles of triangles. It originated over 4000 years ago and was used to calculate sundials. Important trigonometric functions include sine, cosine, and tangent, which relate the sides of a right triangle to its angles. Trigonometry has many applications in fields like construction, astronomy, navigation, and engineering.

1. TRIGONOMETRY
Class 10
Prepared By:
Sharda Chauhan
TGT Mathematics

2. WHAT IS TRIGONOMETRY?
•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.

3. HISTORY
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•
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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.

4. RIGHT TRIANGLE
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A triangle in which one angle is
equal to 900is 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

5. 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

6. TRIGONOMETRIC RATIOS
➢Sine (sin)
➢Cosine (cos)
➢Tangent (tan)
➢Cosecant (cosec)
➢Secant (sec)
➢Cotangent (cot)
Opposite side / Hypotenuse
Adjacent side / Hypotenuse
Opposite side / Adjacent side
Hypotenuse / Opposite side
Hypotenuse / Adjacent side
Adjacent side / Opposite side

7. 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

8. VALUE OF TRIGONOMETRIC FUNCTIONS

9. TRIGONOMETRIC IDENTITIES
Half Angle Identities

10. 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.

11. REAL LIFE APPLICATIONS OF TRIGONOMETRY

14. 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.