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VeroZarate Group Title

Find an exact value: cos(pi/12)

  • one year ago
  • one year ago

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  1. mathmate Group Title
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    let y=cos(pi/12), then apply the double angle formula: cos^2(x)-sin^2(x)=cos(2x) or, substituting sin^2(x)+cos^2(x)=1, 2cos^2(x)-1=cos(2x) cos^2(x)=(1+cos(2x))/2 let x=pi/12 then cos^2(pi/12)=(1+cos(pi/6))/2 Since cos(pi/6) is known to be sqrt(3)/2, cos(pi/12)=sqrt((1+sqrt(3)/2)/2)

    • one year ago
  2. VeroZarate Group Title
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    im sorry but thats not one of my options

    • one year ago
  3. VeroZarate Group Title
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    i somehow have to use the sum and difference formulas

    • one year ago
  4. mathmate Group Title
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    Are they in numerical values?

    • one year ago
  5. VeroZarate Group Title
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    yes they all have sqrt6 and sqrt2 over 4 but with different signs +/-

    • one year ago
  6. mathmate Group Title
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    cos^2(x)-sin^2(x)=cos(2x) is from the double angle formula.

    • one year ago
  7. VeroZarate Group Title
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    how would you split pi/12? i think thats what i need to do?

    • one year ago
  8. mathmate Group Title
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    You will need to evaluate each option to see if it evaluates to: sqrt((1+sqrt(3)/2)/2) which can be written as sqrt((2+sqrt(3)/4) or sqrt(2+sqrt(3))/2 Why don't you post the options if you're not sure?

    • one year ago
  9. VeroZarate Group Title
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    ok i think i got it thanks!!

    • one year ago
  10. mathmate Group Title
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    yw! :)

    • one year ago
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