Question

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

Answer 1

You do math too? D:

Answer 2

Mujhe bhi yaqeen nahi horaha :P

Answer 3

looks like there are two
http://www.wolframalpha.com/input/?i=sin%28x%2F2%29%2Ccos%28x%29+domain+0..2pi

Answer 4

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

Answer 5

1/2x=sin^2x/2

Right ?

Answer 6

cosx= 1-2sin^2 (x/2)

Answer 7

you get a quadratic.. solve for x..

Answer 8

2sin^2(x/2)+cosx-1=0

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

eh,2t-1=0=)t=1/2 t+1=0=)t=-1

Answer 13

yup!

Answer 14

Sin(x/2)=1/2

Sin(x/2)=-1

Answer 15

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..

Answer 16

it was Sin x/2

Answer 17

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

Answer 18

Oh so,

sin x/2 =cos x ?

Answer 19

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

Answer 20

em BOREEEEEED.

Answer 21

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

Answer 22

cosx= 1-2sin^2 (x/2) @hba missed the two..

Answer 23

thik hai? @uri

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

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

Answer 31

@uri 2.. final!

Answer 32

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

Answer 33

@uri its sin(x/2) = -1

Answer 34

k.

Answer 35

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

Answer 36

@sirm3d 2 solutions?

Answer 37

yup. (C) 2

Answer 38

are kitni baar puchegi? @uri :P

Answer 39

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

Answer 40

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

Answer 41

huh!

Answer 42

You have 2 now :P

Answer 43

haha.. he's got 2 now too!

Answer 44

Happy? :D

Answer 45

ha! yes.. :P

Answer 46

Yw xD