In this ppt we basically gives application of Trigonometry in data science and Artificial intelligence

1. Team Aryabhata
APPLICATION OF TRIGONOMERTY
“Mathematicsmaynotteachushowtoaddloveor
minushate. Butitgivesuseveryreasontohopethat
everyproblemhasasolution.”

2. Contributions of Aryabhata in Mathematics:
He formulated the tables of sine.
He introduced the alphabetical counting system.
He was the first to do calculations on the square and cubic roots.
He gave the solutions to equations by r = ax + ca by = ax – c
He was the first to provide the approximate value of π.
He was the one who said that it is an irrational number.
He was the first to sum the first n integers.
And many more like this……
About Aryabhata
Aryabhata was a famous mathematician and astronomer during the
Gupta period. He is credited with the discovery of the 'decimal' system.
For the first time in Indian history, he analysed astronomy and
mathematics as two distinct fields of study.

4. INTRODUCTION
 Trigonometry is a branch of mathematics
that deals with the relationships between
the angles and sides of triangles,
particularly right triangles.
 The word "trigonometry" is derived from
the Greek words "trigonon" (triangle) and
"metron" (measure).
 Ancient astronomers and mathematicians
used trigonometric principles to study
celestial bodies and navigate the seas.

5.  Applications ofTrigonometry
 Trigonometry has been used in a varietyof fields throughout history, including
architecture, theoretical physics, and surveying.
 It can be used for a varietyof things, including:
1. Oceanography, seismology,meteorology,physical sciences, astronomy,acoustics,
navigation,electronics, and many other subjects are among them.
2. It may also be used to determine the length of lengthyrivers,measure the
heightof a mountain, and so on.
3. Solar, lunar, and stellar locations have all been calculated using
spherical trigonometry.
 Trigonometry is used in measuring the height of a buildingor a mountain.
 The distance of a building from the viewpoint and the elevationangle can easily
determine the height of a building using the trigonometricfunctions.

6. Height and distances
Trigonometry is used to find the height, distance
and depth of anything easily by certain
fundamental.
Angle of elevation: It the angle made with the
horizontal when the observer raises his eyes
position .
Angle of depression: It the angle made with the
horizontal when the observer lowers his eyes
position.
It's a very easy technique.

10. Q 1. The angle of elevation of the top of a tower from a point At the
foot of the tower is 30°. And after advancing 150mtrsTowards the
foot of the tower, the angle of elevation becomes 60° . Find the
height of the tower?
Sol: Tan 30° = 1/√3= h/d - - - (1)
Tan60°= √3= h/(d – 150) - - - (2)
From(1)
d = h√3
From(2)
√3 (d – 150) = h
Substituting the value of ‘d’....
√3(h√3 – 150) = h
3h – 150√3 = h
3h – h = 150√3
2h = 150√3
h= 129.9m
 Problems
h
150m
d

11. Sol: Let AB be the tower and the
angle of elevation from point C (on
ground) is 30°.
In ΔΑΒC,
(AB)/(BC) = tan 30°
(AB)/30 = 1/√3
AB = 30/√3 = 10√3 m
Therefore, the height of the tower is
10√3 m.
Q 2. 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.
30m
Q 3. 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 AABC,
(AB)/(AC) = sin 30°
(AB)/20 = ½
AB = 20/2 = 10m
Therefore, the height of the pole is 10 m.
A
B
A
B

12. Trigonometry has diverse applications across various
branches of Artificial Intelligence:
 1.*Computer Vision:* - Trigonometric functions help calculate
angles, distances, and spatial relationships between objects in
images or videos.
- Rotational transformations, such as rotation matrices using sine
and cosine, are essential for image transformations.
 2.*Robotics:* - Trigonometry is fundamental for robot kinematics,
determining the position and orientation of robotic arms and joints.
- In path planning, trigonometric calculations assist in finding
optimal trajectories for robot movements.
 3.*Signal Processing:* - Fourier Transforms, which heavily
involve trigonometry, are used for signal analysis and feature
extraction in tasks like speech recognition and Image processing.

13.  4.*Image Processing:* - Trigonometry is applied in image
transformation and manipulation, such as rotation and scaling.
 5. *Machine Learning:* - Trigonometric functions are
included in feature engineering, capturing complex patterns
in data.
- Sine and cosine functions can be used in neural network
architectures, aiding in the modeling of periodic behaviors.
 6.*Natural Language Processing (NLP):* - Trigonometry
is applied in syntactic analysis, aiding in parsing and
understanding sentence structures.

14.  7.*Reinforcement Learning:* - Trigonometry is used in
modeling agent-environment interactions, especially in scenarios
where angles and directions are critical.
 8.*Optimization Algorithms:* - Trigonometric functions are
used in optimization tasks, such as gradient descent, to find the
minimum or maximum of a function efficiently.
 9.*Simulation and Gaming:* - Trigonometry helps to model
realistic movements, angles, and trajectories in simulations and
video games.

15. 10.*Sensor Fusion:* - In combining data from different sensors,
trigonometry is crucial for accurately estimating object positions
and orientations.
11.*Physics Simulations:* -Trigonometry plays a role in
simulating physical phenomena, especially in areas like
physics-based simulations where understanding angles and
trajectories is essential.
12.*Activation Function:* -Trigonometry functions, such as
the hyperbolic tangent(tanh) and sine, have been used as
activation functions in neural networks, influencing how
information is passed between Neurons.
These applications highlight the versatility of trigonometry in enhancing the capabilities of AI
systems across a wide range of domains.

16. Trigonometry has many Roles in data science:
Data visualization: Trigonometry is used to create and manipulate
graphical representations of data, such as charts, graphs, maps, and
animations. It is also used to perform geometric transformations,
such as scaling, rotating, and translating, on data objects. 📊📊📊
Data analysis: Trigonometry is used to perform various
Mathematical operations on data, such as calculating distances,
angles, slopes, areas, and volumes. It is also used to apply
trigonometric functions, such as sine, cosine, and tangent, to
model periodic phenomena, such as waves, cycles, and
oscillations. 📊📊📊
Data mining: Trigonometry is used to discover patterns and trends
in large and complex data sets, such as text, images, audio, and
video. It is also used to measure the similarity and dissimilarity
between data points, such as using cosine similarity or Euclidean
distance. 📊📊📊

17. Spatial Analysis: Trigonometry is used in tasks that
Involves spatial data analysis, such as understanding the
orientation or relative positions of objects.
Time Series Analysis: Trigonometric function are used
sometimes employed to model periodic patterns in
time series data.
These are some of the examples of how trigonometry is used in various aspects of
data science. Trigonometry is a useful and essential tool that can help us explore and
understand data in different ways. 📊📊📊

18. 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.
 Trigonometric function are the relationships amongst various sides in
right triangles.
 The enormous number of application of trigonometry include astronomy,
geography, optics, electronics, probability theory, statistics, biology,
medical imaging (CAT scans and ultrasound), pharmacy, seismology,
land surveying, architecture .

19. THANK YOU SO MUCH FOR
YOUR VALUABLE TIME…..
BY:
Abhishek Gupta
MuskanVerma
Nayan Pandey
Sufiyan Zamindar
Kaif Khan
THANK YOU SO MUCH FORYOUR
VALUABLETIME…..