uri
Halp meh pliss,
The number of positive values of x less than 360 degrees which satisfy the equation sin 1/2x =cos x is?
a)0 b)1) c)2 d)3 e)4



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saifoo.khan
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You do math too? D:

hba
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Mujhe bhi yaqeen nahi horaha :P


yrelhan4
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3
write cosx in terms of sin^2 x/2 and solve!

uri
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0
1/2x=sin^2x/2
Right ?

yrelhan4
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3
cosx= 12sin^2 (x/2)

yrelhan4
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3
you get a quadratic.. solve for x..

uri
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0
2sin^2(x/2)+cosx1=0

yrelhan4
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3
2t^2 + t 1=0 where t=sin(x/2)

uri
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0
Quad,breaking the middle term or completing the square method?

yrelhan4
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3
breaking the middle term.. you would get (2t1)(t+1)=0 where t=sin(x/2)

uri
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eh,2t1=0=)t=1/2 t+1=0=)t=1

yrelhan4
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3
yup!

uri
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0
Sin(x/2)=1/2
Sin(x/2)=1

yrelhan4
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3
so there would be 3 values of x/2 in 0 to 360.. 30,120,270. so x=60,240,540.. since you want from 0 to 360.. there would be 2 solns..

uri
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0
it was Sin x/2

yrelhan4
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3
if sin(x/2) = 1/2 , what is x? 0>x>360

hba
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1
Oh so,
sin x/2 =cos x ?

yrelhan4
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3
1 sin^2(x/2)= cosx @hba

uri
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0
em BOREEEEEED.

yrelhan4
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3
look.. let x/2=k .. sin(k)=1/2 > k=30, 120.. > x=60, 240

yrelhan4
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3
cosx= 12sin^2 (x/2) @hba missed the two..

yrelhan4
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3
thik hai? @uri

sirm3d
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@yrelhan4 since \(\displaystyle 0 \leq x \leq 360\) then \(\displaystyle 0 \leq \frac{x}{2} \leq 180\)

sirm3d
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now, \(\sin x/2 = 1/2\) therefore \(x/2=30, 150\) or \(x=60, 300\)

uri
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Yrelhan GUESSSS WHAT?! I donyt undastand aaaanythang nd ima sho confuzzeld tooh,I caant eveen speel corractly. o.O

yrelhan4
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3
lol.. i am such a fool.. you are right! @sirm3d

uri
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0
Wut iz the aaansweeer?! none of my option matches your answer!

yrelhan4
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3
i just wrotw150 value wrong, right? why am i a fool then? :P

sirm3d
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2
the other equation, \(\sin x/2 = 1\) has no solution in \(0 \leq \frac{x}{2} \leq 180\)

yrelhan4
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3
@uri 2.. final!

uri
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@sirm3d sinx/2=1 has no solution so we will leave it? xD

yrelhan4
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3
@uri its sin(x/2) = 1

uri
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0
k.

sirm3d
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2
@uri, just count the number of solutions: \(x=60^0,\;300^0\)

uri
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@sirm3d 2 solutions?

sirm3d
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2
yup. (C) 2

yrelhan4
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3
are kitni baar puchegi? @uri :P

uri
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AMG THANKYOUUUUUUUUUUUUU!AMG THANKYOUU SOO MUCHHHHH!!!! :D

yrelhan4
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3
mera medal.. :'( .. aadha to maine solve kiya..

yrelhan4
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3
huh!

uri
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0
You have 2 now :P

yrelhan4
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3
haha.. he's got 2 now too!

uri
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0
Happy? :D

yrelhan4
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3
ha! yes.. :P

uri
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0
Yw xD