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AravindG

  • 3 years ago

how to find value of sin 18

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  1. Argonx16
    • 3 years ago
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    Take a calculator, and hit the "sin" button and type 18 in. You (may) need a scientific/graphing/google calculator. If you are asking how to do so by hand, I am not qualified to tell you.

  2. AravindG
    • 3 years ago
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    there must be a method using the formulas

  3. AravindG
    • 3 years ago
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    turing??

  4. TuringTest
    • 3 years ago
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    I am thinking....

  5. SUROJ
    • 3 years ago
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    (18*5)=90

  6. AravindG
    • 3 years ago
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    so?

  7. TuringTest
    • 3 years ago
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    all I got is the fact that we can write this as\[\sin(\frac\pi{10})\]thinking if we can go somewhere from there...

  8. TuringTest
    • 3 years ago
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    looking at some way to write this such that we can apply an identity to it...

  9. SUROJ
    • 3 years ago
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    http://answers.yahoo.com/question/index?qid=20061025091609AASJNUn

  10. AravindG
    • 3 years ago
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    whoa!!

  11. TuringTest
    • 3 years ago
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    why is \[\sin(3x)=\cos(2x)\]?

  12. SUROJ
    • 3 years ago
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    Most of peoples are not smart....they are clever

  13. campbell_st
    • 3 years ago
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    use the power series expansion \[\sin(x) = x/1! - x^3/3! + x^5/5! -x^7/7!.....\]

  14. AravindG
    • 3 years ago
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    hw put valu 18>??

  15. AravindG
    • 3 years ago
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    bt it goes on

  16. SUROJ
    • 3 years ago
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    if x= 18, 2x+3x=90

  17. AravindG
    • 3 years ago
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    Another way to do this is to start with a regular pentagon where the length of each side is one unit. I'll outline the steps. (You can fill in the details.) Call the pentagon ABCDE. Draw diagonals AC and BE, which intersect at point F. Using the fact that each angle of the pentagon is 108 degrees, you can prove the triangles BFC and AFE are isosceles. Therefore the lengths of line segments CF and EF are also 1 unit. Also note the angles for the triangles are 72-72-36. Now show that ABF and CAB are similar triangles. Since they are similar, this means BE/AB = AB/BF. Since BE = EF + BF, substitute to get (EF + BF)/AB = AB/BF. Let's define x to be the length of BF. Then, since EF = 1, the equation becomes (1 + x)/1 = 1/x, or x^2 + x - 1 = 0. Use the quadratic equation to get x = (sqrt(5) - 1) / 2. Finally, let's create an 18-72-90 by drawing the altitude of triangle BFC from vertex C to side BF. Since BC = FC, the altitude hits BF at the midpoint of BF, which we will call point G. So, (a) triangle GBE is an 18-72-90 triangle, (b) BG = BF/2 = x/2. Using this 18-72-90 triangle, sin 18 degrees = BG / BC = x/2. Therefore sin 18 = (sqrt(5) - 1) / 4.

  18. AravindG
    • 3 years ago
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    i liked this

  19. SUROJ
    • 3 years ago
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    2x=90-3x

  20. SUROJ
    • 3 years ago
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    cos both side

  21. AravindG
    • 3 years ago
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    k

  22. SUROJ
    • 3 years ago
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    cos(2x)=sin(3x)

  23. AravindG
    • 3 years ago
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    thx evryone

  24. SUROJ
    • 3 years ago
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    catch it?

  25. TuringTest
    • 3 years ago
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    gotchya, thx

  26. AravindG
    • 3 years ago
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    campbell pls tell ur method

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