Concepts (Part - 1) - Trigonometric Functions, Math, Class 11 Video Lecture

hello friends this video on inverse
trigonometric functions part 1 is
brought to you by exam fear calm no more
fear from exam what we will study we
will study inverse geometric functions
and properties of inverse to limited
functions before we study inverse
trigonometric functions let's understand
why do we need to study inverse
trigonometric function what is the
practical application of inverse
trigonometric function what will happen
if you don't study inverse relation so
we'll study here what is the application
of inverse trigonometric functions in
day-to-day life if you see this in the
world of science and technologies we do
use inverse trigonometric functions lot
of time for example you want to find the
angle the star makes with the place or
you will find in the molecular structure
the angles which these molecules made
for such things we need inverse
trigonometric function we don't know
inverse trigonometric functions we won't
be able to deal with such scenarios in
terms of sines and equinoxes also if you
are not attacked and you are building
some monuments or buildings in that case
also you need inverse geometric
functions for example you want to find
the angle with which the Subban lorem
this angle or this angle for such thing
we need inner still minute difference so
if you an architect or if you are in the
field of science inverse trigonometric
function is a must for you before we
start with in course dramatic function
let's see the dilemma and that is the
dilemma which is the foundation for the
whole chapter the dilemma is like this
we know that for inverse to exist the
function must be 101 and Aundre if you
don't know this please watch the
previous chapter reduce in this chapter
we have explained why the change should
be 101 and Anto or inverse to exist so
the statement we know is for inverse to
exist function must be
101 and autumn if you don't know what's
the nature if you know you can proceed
with them next time but we know that the
trigonometric functions they are neither
101 not only on their national domain
please note on their nashville domain
and range they are neither 101
order but we have to find inverse
trigonometric function how can we do we
can't do we have to write something do
something something we have to do to
make sure that trigonometric function is
101 and on why we want to move that
because we want to find inverse
trigonometric function you got dilemma
right the dilemma is for a fun for
inverse to exist the function to be has
to be 101 and fondo but we are saying
that take no my tip no metric functions
are neither 101 long order but still we
want to find inverse trigonometric form
if you see this what I'm trying to say
is it never is a sine X graph you know
that sine Phi is you know in fact sine 0
is also 0 sine minus pi is also 0 small
special so if you make this crap like
this there are values like 0 pi minus PI
to PI all these will give you values
here correct so and physically your
there are so many values like PI by 2
this gives one so there's so make a plus
if you see minus PI by 2 so 5 PI by 2
this will also give 1 so you see this is
not 1 over Y because for one value there
are so many injections so it is not
vulnerable also it is not on to Y
because the sine value if you see the
maximum
as one many of us - also won 2-1 in the
range for this there are so many values
like 4 5 6 from talking about our to our
domain and range in that is if you see
these rebels are all awesome because the
national domain is nothing but I do I so
if you see in this natural domain and
range
it is neither 101 non and we want to
find inverse of this function which we
cannot do now because it is not 1 1 it
is neither one hour nor Anto so what
should we do we should restrict these
domain and range if you restrict this
domain and range then only we can make
this techno metric function as inverse
we can find the inverse of trigonometric
function if and only if if we restrict
restrict what drastic domain and so if
you restrict domain and range what will
do you will make this function 101 and
all let's explain all this thing will
take some example sine cos of and we'll
get some examples to do that just try to
understand this why we are doing it for
a function for inverse to exist for a
function function has to be 101 and Anto
but we know that for trigonometric
function they are neither Benoa not on
top on their master and domain and range
we saw this there are some extra values
and so many balance pointing to 0 so it
is not 101 not under but we want to make
it inver scible because you want to find
inverse the global function to do that
what we are doing is we will restrict
this domain and will list in this place
and thus will make the function 101 and
order let's see the same things you do
the restrict domain and range to make
sure that the inverse
so in this case if you see if you
restrict this value from the example
from here to here you see goes to zero
on one and it goes to against it and
then I have some negative values also so
I'd take these or better let me take
this farm so in this hub you see all the
values which I am getting the y-axis are
unique values so if my in my domain is
this and my range is minus 1 to 1 in
that case I am getting in vertical
function in that is it real 1:1 and onto
function
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