Page 37 - nai udaan march 2024

Mathematical functions Sine and Cosine Functions: Unveiling the
Mathematical Dance of Swinging Motion
Imagine you're on a camping trip with your
Various mathematical functions are used for friends, and you decide to set up a makeshift
different purposes, ranging from data
preprocessing to model optimization. swing using a long rope tied to a sturdy tree
A function essentially describes how one quantity branch. As you swing back and forth, your
(the dependent variable) depends on or varies friend standing nearby notices something inter-
with another quantity (the independent esting: your motion seems to follow a certain
variable). Functions provide a systematic way to pattern, almost like a dance with the wind.
express relationships between variables, allowing
us to analyze and understand the behavior of Curious, your friend takes out their phone and
various phenomena in mathematics and the starts jotting down some measurements. They
sciences. notice that your swinging motion can be

described using a mathematical function called a
For example, let's consider a simple function:
f(x) = 2x+ 3 sine wave. They explain that the sine function
In this helps us understand how things move in a periodic
function, x is or wave-like manner, like the up and down
the indepen- motion of your swing.
dent variable,
and f(x) is the As you swing higher and faster, your friend
dependent points out that the cosine function comes into
variable. This play, describing the horizontal movement of
function tells your swing. Together, these mathematical tools
us that for any help your friend predict your swinging trajectory
given value of
x, the and even calculate how high you'll go with each
corresponding value of f(x) is obtained by swing.
multiplying x by 2, then adding 3. So, the
function describes a linear relationship between Thanks to the power of sine and cosine functions,
x and f(x). what started as a simple camping trip turned
into a fascinating lesson in math and physics,
Functions can take many different forms and can be showing how these tools help us make sense of
used to model a wide range of relationships, from the world around us, even in the most unexpected
simple linear relationships to complex, nonlinear situations.
ones. They are fundamental tools in mathematics
and are used extensively in various fields,
including physics, engineering, economics, and
computer science, to describe and analyze
real-world phenomena.

Let's use a combination
of sine and cosine
functions to draw a
basic flower shape on
graph paper using the
Wolfram Alpha AI
tool.

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