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Math4Life Group Title

Use a half–angle identity to find the exact value of sin 105°

  • one year ago
  • one year ago

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  1. baziham Group Title
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    i completely answered to you. you must use sin and cos formula and use 105=90+30/2 sin(a+b)=.. sin(2a)=.. cos(2a)=.. try it

    • one year ago
  2. Math4Life Group Title
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    Ok i'm trying it right now

    • one year ago
  3. Math4Life Group Title
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    I got -0.260736296 and I have a feeling its not right

    • one year ago
  4. jim_thompson5910 Group Title
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    they want the exact value, not an approximation

    • one year ago
  5. Math4Life Group Title
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    Yes exact value

    • one year ago
  6. jim_thompson5910 Group Title
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    Hint: Use the half angle formula \[\Large \sin\left(\frac{\theta}{2}\right) = \sqrt{\frac{1-\cos(\theta)}{2} }\]

    • one year ago
  7. Math4Life Group Title
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    I'm so confused

    • one year ago
  8. jim_thompson5910 Group Title
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    notice how 105 = 210/2

    • one year ago
  9. Math4Life Group Title
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    and 210/2 is 105

    • one year ago
  10. Math4Life Group Title
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    so are you saying 210 is my answer?

    • one year ago
  11. jim_thompson5910 Group Title
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    no, I'm saying the fact that 210 (which is an angle found on the unit circle) divided in half gives you 105

    • one year ago
  12. jim_thompson5910 Group Title
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    so sin(105) = sin(210/2)

    • one year ago
  13. jim_thompson5910 Group Title
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    then you would use that formula I gave above

    • one year ago
  14. jim_thompson5910 Group Title
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    I'll get you started Start with this fact \[\Large \sin(105) = \sin\left(\frac{210}{2}\right)\] Then use the formula given previously to get \[\Large \sin(105) = \sqrt{\frac{1-\cos(210)}{2} }\] Then use the unit circle to evaluate cos(210) and simplify as much as possible

    • one year ago
  15. Math4Life Group Title
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    Ok I understand

    • one year ago
  16. baziham Group Title
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    where \[\cos(210)=\cos(180+30)=\cos(180)\cos(30)-\sin(180)\sin(30) \]

    • one year ago
  17. baziham Group Title
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    answer is \[\sqrt{\frac{ 1-\left\{ \cos(180)\cos(30)-\sin(180)\sin(30) \right\} }{ 2 }}\]

    • one year ago
  18. baziham Group Title
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    real answer is: 0.9659258262890682867497431997289

    • one year ago
  19. baziham Group Title
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    and you can solve above equation and get parametric answer can you do?

    • one year ago
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