## uri 2 years ago 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

1. saifoo.khan

You do math too? D:

2. hba

Mujhe bhi yaqeen nahi horaha :P

3. satellite73

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

4. yrelhan4

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

5. uri

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

6. yrelhan4

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

7. yrelhan4

you get a quadratic.. solve for x..

8. uri

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

9. yrelhan4

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

10. uri

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

11. yrelhan4

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

12. uri

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

13. yrelhan4

yup!

14. uri

Sin(x/2)=1/2 Sin(x/2)=-1

15. yrelhan4

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..

16. uri

it was Sin x/2

17. yrelhan4

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

18. hba

Oh so, sin x/2 =cos x ?

19. yrelhan4

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

20. uri

em BOREEEEEED.

21. yrelhan4

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

22. yrelhan4

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

23. yrelhan4

thik hai? @uri

24. sirm3d

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

25. sirm3d

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

26. uri

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

27. yrelhan4

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

28. uri

29. yrelhan4

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

30. sirm3d

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

31. yrelhan4

@uri 2.. final!

32. uri

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

33. yrelhan4

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

34. uri

k.

35. sirm3d

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

36. uri

@sirm3d 2 solutions?

37. sirm3d

yup. (C) 2

38. yrelhan4

are kitni baar puchegi? @uri :P

39. uri

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

40. yrelhan4

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

41. yrelhan4

huh!

42. uri

You have 2 now :P

43. yrelhan4

haha.. he's got 2 now too!

44. uri

Happy? :D

45. yrelhan4

ha! yes.. :P

46. uri

Yw xD