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VeroZarate

  • 2 years ago

Find an exact value: cos(pi/12)

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  1. mathmate
    • 2 years ago
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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)

  2. VeroZarate
    • 2 years ago
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    im sorry but thats not one of my options

  3. VeroZarate
    • 2 years ago
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    i somehow have to use the sum and difference formulas

  4. mathmate
    • 2 years ago
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    Are they in numerical values?

  5. VeroZarate
    • 2 years ago
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    yes they all have sqrt6 and sqrt2 over 4 but with different signs +/-

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

  7. VeroZarate
    • 2 years ago
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    how would you split pi/12? i think thats what i need to do?

  8. mathmate
    • 2 years ago
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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?

  9. VeroZarate
    • 2 years ago
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    ok i think i got it thanks!!

  10. mathmate
    • 2 years ago
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    yw! :)

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