Our math teacher is going to explain you
sine cosine and tan in a way that even a
small kid can understand it easily.
Let's take an example of a forest
officer who wants to
measure a height of this tree the tree
is very big so he doesn't want to climb
on it because it's just too much work.
And he's going to use the knowledge of
sine cosine and tan
to come up with the height of this tree
very easily.
So first he will measure the distance
between himself
and the tree let's say it is 50 feet
then he has an instrument
using which he can measure an angle
between the ground
and the top the notch of the tree you
know from where he's
looking so let's say that angle is 30.
having this knowledge now you can figure
out
the tree of the height of the tree and
we'll see how.
Let me represent this as a right angle
triangle
so here right angle triangle is
something where this particular angle is
90 degree
and i'm just taking an example here.
let's say the height is 3 and the base
is 4. For such a triangle
the angle this angle will always be
36.87 that's like the law of nature
what is law of nature well 2 plus 3 is
always 5
that is law of nature similarly if you
have a triangle right angle triangle
with
height 3 base 4 this angle will always
be
36.87. If your height is 4
the angle will always be 45 if your base
is 5 the angle will always be 38.65 so
it's kind of a
fix mapping that nature has
can we represent the relation between
this angle and these two
sides in a mathematical form.
That is what mathematicians do they
conduct scientific experiments
and then they find some relationship and
they just
give a name to those relationships. So
sin theta, cos theta is not a rocket
science really
it's just a relationship. It's a name
that they
gave to some natural law
so 36.87 is related to three and four.
We can also say that 36.87 is related to
the ratio between three and four
because if you change this ratio this
angle will change.
And if the ratio is constant let's say
if three by four is points indeed
75 then this relationship is kind of
constant you know
so mathematicians give this
relationship a name tangent.
They call this tan theta okay? So
10 of 36.87 is 0.75
and you all know 0.75 is opposite side
divided by h is inside. Therefore
tan theta is opposite side by adjacent
side. You
you have studied this in your math class
but I just
represented the whole concept in a
little different way so that you
understand that
it's a natural law to which
mathematician gave this fancy name
called
tangent. If you take different triangle
then you will find the tangent of 10
degree is 0.176 this is fixed.
It's like a fixed mapping 1045 is
always one if you so basically you can
create
this kind of mapping table you know 10 1
is 0.0174 this is
fixed mapping that exist in nature if
you want to find out
tan of any angle you can go to this
website rapidtables.com. I encourage you
to try it out
try out different angles and you'll find
that 10 30 is always 0.577
It's like always fixed mapping now let's
use that to solve our problem so we know
that tan data is opposite side here by
adjacent side
here opposite side is x angle is 30
adjacent side is 50 feet you can use
your mapping table
and oh yeah 10 30 is 0.577.
Substitute that here and you all are
I think good with this level of basic
math.
You can figure that the height is 28.85
[Music]
okay so 28.85 this forest officer if
he or she studied math properly during
the school or high school days.
They will be able to figure this out and
they will save a lot of effort
of measuring height of the three you can
realize now that you know 10 to that
cost
these are not just the concept you study
in the school
they have real life application. How
about sine and cos now.
A curious cat is now asking this
question
in order to understand that you need to
understand Pythagoras theorem
so there was this uncle very wise uncle
called Pythagoras.
He existed in back in
I don't know like few years many years
back actually
so he invented this Pythagoras theorem
which says that the square of Hypotenuse
is equal to the square of
individual side and you just sum it up.
So here,
the square of the individual sides is 25
and
hypotenuse is 5 basically so that's the
Pythagoras theorem. Very basic. You
probably know about this already now
let's see.
Let's try to understand sine and cosine
by taking another real life example.
Let's say you have a heavy package lying
in front of your home
and you want to drag it inside your room.
I know you will have stairs etc but
let's say the
surface is flat you can attach a rope to
it and you can try lifting
it now let's say you are putting a 10
newton
force. You know newton is a is a unit of
measure for
force and then there is some angle all
right so there is a 30 degree angle
now part of this force goes into x
direction
and part of that force goes into y
direction.
And x direction is nothing but the
component of the force that is used to
pull the box in a horizontal position
and
y(f) is the force that is used to lift
the package a little bit
you need to lift it a little bit so that
you can address the
friction between the package and the
ground. If you just
keep the rope very straight like you
know
like like horizontal then it might be
hard to pull the package
if you don't trust me like just try this
out at your home you will find it hard
you need to lift it little bit so that
the friction between package
and the ground can be reduced. Now you
need to apply
exit right amount of force so so that
you can lift this package
you know with a less effort. And here
to find the components you know the
component the tan newton force has two
component
x component, y component and you can find
this using
sine and cosine and we'll see how okay?
So now here's the situation
and first let me try the let me find the
component that's really
used to pull this package up.
Alright! now in this beautiful picture
you again know that
it's a law of nature that this angle 30
this tan newton
y of x(f) they are all related it is also
a law of nature
that if you know this 10 newton and 30
degree angle
just these two you can actually find
y s and that law is expressed as
sine so sine theta is basically
opposite side divided by hypotenuse
so that's your equation and again
if you do sine 30s it's a fixed mapping
sine 30 is
always 0.5 since the big bang,
since the universe existed, sine 30 has
always been 0.5 my friend
and if you don't believe me again go to
this website try out.
You'll see sine 30 is 0.5. Okay let's put
that into equation
0.5 and with easy math you can figure
out that the
vertical component with 30 degree will
be 5 newton.
similarly x f so x f has a different
relationship
and it's called cosine. Cosine is always
adjacent
side divided by the hypotenuse.
And that's gonna be cos 30 is
always again 0.866.
Ad that's going to be 8.66
roughly so now again if I studied math
sine, cosine
etc really well during my math class
maybe I will be able to pull or
or push whatever this package really
well. You know this is a very primitive
example by the way
but sine, cosine and tangent are used
heavily in mechanical engineering, civil
engineering different branches. You know
these are the concept there they have a
real life
application so just to summarize these
are the equations of sine, cosine
and tan. And as this video is part of the
series
on I have this series called math for
data science
now why is this video part of that math
for data science well
in data science you will learn about
cosine similarity
which is used in natural language
processing. So before you study cosine
similarity I thought
I would give you a good understanding of
sine cosine and tan.
If you like this video please give it a
thumbs up and if you have any comment
post in a comment box below.
Thank you for watching.