## amruta1997 3 years ago how to find value of sin 18.......plz explain in detail

1. Rezz5

without the use of the calculator?

2. amruta1997

ya

3. amruta1997

how 2 derivate it

4. Rezz5

taylor expansion can estimate it for you

5. amruta1997

i did not get what u want to say

6. amruta1997

sauravshakya u may try

7. amruta1997

who is taylor

8. Rezz5

Taylor Expansion is the way of estimating and function sinx is $x-\frac{ x ^{3} }{ 6 }+\frac{ x ^{5} }{ 120 } -...+...$

9. sauravshakya

5*18=90 sin(5*18)=sin90 Let x=18 then, sin(5x)=sin90

10. amruta1997

i think u r wrog somewhere

11. sauravshakya

U can proceed from here but this will be too long but it will give u exact value.

12. amruta1997

we dont have a formula for sin 5 thete

13. sauravshakya

From sin(5x)=1 u need to find the value of sinx

14. amruta1997

i mean to say we dont have its expansion

15. sauravshakya

sin(5x) = sin(2x + 3x) = sin2x * cos3x + cos2x * sin3x

16. amruta1997

hmmmmm that wd be 22 long

17. gohangoku58

5x= 90 2x+3x=90 3x=90-2x sin 3x= cos 2x now put formula of sin 3x and cos 2x in terms of sin x only.

18. amruta1997

hmmmmmm this wd b an easy one

19. Rezz5

18=Pi/10 sin(Pi/10)=0.3090169944 F[x]$=x-\frac{ x ^{3} }{ 6 }+\frac{ x ^{5} }{ 120 }-...$ f[Pi/10]==0.3090170542 you decide

20. sauravshakya

Great!

21. amruta1997

but when we will solve the quadrtic equation then we will get two values of sin theta

22. amruta1997

which one is great

23. sauravshakya

@gohangoku58 's one

24. amruta1997

hmmmmmmm

25. sauravshakya

because that gives exact value not approximate

26. amruta1997

hmmmmm but two values

27. amruta1997

which one to select

28. amruta1997

u plz try it once

29. sauravshakya

well, sin 18 lies in first quadrant so take positive value

30. amruta1997

hmmmmm

31. amruta1997

good

32. gohangoku58

u'll get a cubic equation, with one root = 0 (can't be, rejected) and 2 other roots.....from which u select one with positive value..... like saura said...

33. amruta1997

i failed 2 use common sence

34. amruta1997

no not a cubic but a quadratic u try it

35. amruta1997

i tried it jjust now

36. gohangoku58

sin 3x= ?

37. amruta1997

3sinx-4 sin cube x

38. gohangoku58

3sinx-4 sin cube x<----cubic

39. amruta1997

no but sin 2 x is also there

40. gohangoku58

*cos 2x

41. amruta1997

ya

42. amruta1997

1-2sin square x

43. amruta1997

then we can take sin in common

44. sauravshakya

no u cant 1 is there

45. amruta1997

46. gohangoku58

who ?

47. amruta1997

sorry for the personal Q

48. gohangoku58

we both are there...

49. amruta1997

all of u

50. sauravshakya

|dw:1353245978780:dw|

51. amruta1997

may i know ur id's

52. amruta1997

we can contact there also

53. amruta1997

saura i will tell u wait

54. gohangoku58

what say saura ?

55. amruta1997

short form

56. gohangoku58

4 x^3 - 2 x^2 - 3x + 1 = 0 one root is x=1 which can't be.... i made a typo earlier and wrote that one root is 0

57. amruta1997

one moment plzz

58. amruta1997

2 theta=90-3 theta

59. amruta1997

sin 2 theta = cos 3 theta.................sin (90-theta)=costheta