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
•
•
•
•
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
•
•
•
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

15. Line of Sight
Horizontal

16. Angle of Elevation
The angle which the line of sight
makes with a horizontal line drawn
away from their eyes is called the
angle of Elevation of aeroplane from
them.

17. Angel of Elevation
Angel of Elevation

18. Angel of Depression
If the pilot of the aeroplane looks
downwards at any object on the
ground then the Angle between his
line of sight and horizontal line
drawn away from his eyes is called
Angel of Depression

19. Angle of Depression
Horizontal
Angel of Depression

20. Now let us Solve some
problem related to
Height and Distance

21. The angle of elevation of the top of a tower from a
point on the ground, which is 30 m away from the
foot of the tower is 30°. Find the height of the tower.
.
Let AB be the tower and the angle of elevation from point C
(on ground) is
30°.
In ΔABC,
Therefore, the height of the tower is

22. A circus artist is climbing a 20 m long rope, which is tightly
stretched and tied from the top of a vertical pole to the
ground. Find the height of the pole, if the angle made by the
rope with the ground level is 30 °.
Sol:- It can be observed from the figure that AB is the pole.
In ΔABC,
Therefore, the height of the pole is 10 m.

23. Let K be the kite and the string is tied to point P on
the ground.
In ΔKLP,
.
Hence, the length of the string is

24. ,

25. Height of tree =
.
+ BC
Hence, the height of the tree is

28. 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.

29. Any Questions?