Problems Degree radiam Measure, arc angle length -Trigonometry Functions, Mathematics, Class 11 Video Lecture - Class 11 | Best Video for Class 11

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one two three we have to convert 50
degree 20 minutes into Radian ISM so we
know that 20 minute is equal to 20 by 60
degrees because 60 minute is good to one
degree we know this so the strain T 50
degree 20 minute is equal to 50 degree
plus 20 by 60 degree is equal to 51 by 3
think now we have to convert is into
Radian so we know that 360 degree is
equal to 2 pi 1 degree is equal to 2 pi
by 360 radiant this is the radiant so 51
by 3 degree is equal to 51 by 3 we can
also say 150 1 by 3 51 by 3 if you see
here is nothing but 50 into 3 plus 1 1 2
T plus 1 by 3 that is 151 by so 151 by 3
this into 2 pi by 360 radio and this is
nothing but you cancel this this becomes
180 so this become 151 by 540 pi Radian
is the answer now let's convert the
Radian to degree so we have to convert 5
Radian to degree then use the formula
the formula is 2 pi Radian is equal to
360 degrees right so one Radian is equal
to 360 by 2 pi degree so 5 Radian will
be equal to 360 by 2 pi into smile
big all right
so we'll replace pi is equal to 42 by
seven we know this will replace pi by 2
2 by 7 so this guy is equal to 3 60 by 2
into 22 by 7 into Phi DT and that is the
answer if you want we can break this
this becomes Moretti
this becomes 90 missing 11 so this
become 90 into 35 by 11 so if you want
to convert this there becomes 3 1 5 0 by
11 degree on C 1 5 0 this we can say
level by t-150 what is it too deeply you
get 9 just forget 82 9 which is 5 all
right 3 1 5 this becomes 8 80 this is 72
becomes 666 for this is nothing but 286
4 by 11 this is degree we can also write
this as 2 86 degree 4 by 11 into 60 this
becomes minute come because we know that
we know that 1 degree is equal to 60
minutes so this becomes right here to 86
degree and this is 245 11 minute so he
rose if we divide this what you get is
11 why to 14 to 22 20 the sweetums 11190
so you get 21 minute so that is 286
degree 21 minute and nine by 11 against
the minute also see my environment also
become
into six-second by multiplying by 16
this become second so now this also
becomes 960 54 by 11 so you could almost
fight 50 almost 50 because solver 50
because by 40 will say is 444 this
becomes defined from ten hundred with a
99 so this becomes pertaining forty nine
point something you will make almost e
so this becomes 2 86 degree 20 1 minute
50 seconds and that is offensive so what
we have done we have we have seen that
119 is equal to 60 by 2pi so 5 written
in 53 65 2 pi into 5 degree we have
replaced PI by 2 to 2 by 7 so we got dis
minute degree 3 1 5 0 by 11 degree now
we converted we converted this so we
converted this rational part in 2
minutes because 4 by 11 degree is equal
to 4 by 11 to 60 minutes so we got 26
minutes and 50 seconds in this example
we have to find radius if the angle and
the arc is given so the question is find
the radius of the circle in which
central angle is 60 degree and the arc
length is 37 point or you see here the
angle is 60 V and the arc length is 37.4
if we draw the circle it is something
like this this is a circle this is 60
degree and this is 37 point O and we
have to find the R so we know that theta
is equal to l by r where theta is in
Radian so to convert 60 degree in
terrarium so we have to convert 60
degree into x radiant to find X so we
know that 360 degree is equal to 2 pi
Radian so we'll divide
this equation by 6 or 60 degree is equal
to PI by 3 Radian you have got this so
now we'll use formula theta is equal to
L PI R so T type we'll say PI by 3 is
equal to L L is 37.4 we have and we have
to find our or we can say R is equal to
37 point 4 into 3 by PI and PI we can
say 22 by 7 so if we solve this we had
thirty five point seven as the ladies
but if I point seven this is centimeter
so this we also will become setting it
so we have found radius is equal to two
the seven point four centimeter we
have done so we have used theta is equal
to l yr and we know that this in this
formula theta is always in Radian so we
have converted 60 degree gradient and we
got PI by three Radian and we have
placed theta is equal to PI by 3 here is
going to do L 37.4 centimeter by r and
we got our is are you thirty five point
seven centimeters
let's say from a problem of anger art
and radius so the question says the
minute hand up of wash is 2 centimeter
long how far it goes in 15 minute clip
so this is the watch typical watch and
it says that minute hand this guy is 2
centimeter and start with the suppose s
is 12 10 and 50 minute cycle is this
much asking in this duration how far it
goes this is the thing this is a 50
minute 50 minute so we will convert this
into PI now 50 minute so we have to find
this this is our s given we have to find
help so we know that in 60 minute in 60
minute is equal to 2 pi Radian correct
because it is 60 minute it was one
complete cycle
and that is 2pi radium so one minute is
equal to 2pi 60 radium 15 minute is
going to 2pi by 16 into 50 radiant we
cut this cut this this so is equal to 5
by 3 pi Radian
so this 50 minute is nothing but we can
also say 50 minute is going to 5 by 3 pi
Radian now simple we have to use this
formula
I mean theory as well to L where so or
we will say 5 by 3 pi is equal to this
time L we have defined and we have our R
is equal to 2 centimeter so L is equal
to you multiply this by this it becomes
5 into 2 pi against it will you do by 7
and this is this is centimeter because
this is in centimeter so L will also be
in centimeter or we get we solve this L
is going to ten by three and three point
three point three and twenty four seven
three-point-four we get something around
10 point we will take one more problem
based on problem our candidates what a
problem comes and exams on this so let's
clear those are gone Waldemar Canadians
so it says that the arc of same length
of two circle substance angle 45 and 90
degree 80 central find the ratio of
ready that means they are in circle this
is album Jordan
shall say r1 and see the arm of same
length that is length the same so this
guy is L this way also both are l
this.length the same and the angle is
different this guy is 45 degree and this
is
90 degree we have to find ratio of all
online order so we know here theta is
equal to L where so let's first convert
this theta into Radian so we know that
360 degree is equal to two pi Radian so
to get 45 we should divide by a because
360 by 8 is equal to 40 by 8 or 45
degrees is equal to PI by a trillion
similarly 360 degree is going to be 2 pi
Radian we know this we have divided by 4
this time because you are 19 since this
2 by 4 is 1 to 2 pi by 4 or 90 degree is
written by 1 this is PI by 4 sorry
because to 2 by 8 is 4 this is 5 by 2 so
we have got this now theta is go to l by
r so for this we will have let's suppose
theta 1 is going to L 1 by r 1 and for
this theta 2 is going to antibiotic but
we know that L 1 is equal to nd that we
know this and this are same so we'll
write two equations theta 1 is equal to
l by r 1 this equation 1 and theta 2 is
going to L by heart this is equation
will divide is 2 equation we get theta 1
by theta 2 is going to R 2 by R 1
now theta 1 by theta 2 spent world
wherever
so I'll write theta 1 is equal to PI by
4 and theta 2 is equal to PI by 2 is
going to R 2 by R 1
so this if you solve you get this is
cancel and this is of the cancel - so we
get r2 by r1 is equal to 1 by 2 let's
see what we have
first you have converted this degree to
Radian and then we have got this two
equation theta one is get to l by ro
theta two is equal to l by r 2 and now
we divided equation 1 and equation 2 you
get the answer
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