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glucy7

  • 2 years ago

Find the exact value by using a half-angle identity. cos(5π/12) I know someone knows how to do this! if you could explain too, that'd be great!

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  1. anas2000
    • 2 years ago
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    os 5π/12 cos ((5 pi/6)/2) = +/- sqrt( (1+cos (5 pi/6))/2 ) cos(5 pi/6) = -sqrt(3)/2 cos (5 pi/12) = +/- sqrt( (2/2-sqrt(3)/2)/2 ) cos (5 pi/12) = +/- sqrt( ((2-sqrt(3))/2)/2 ) cos (5 pi/12) = sqrt( ( (2-sqrt(3))/4 ) ) 5 pi/12 is in quadrant 1 so we choose the + sign because cos is positive there

  2. glucy7
    • 2 years ago
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    thank you!!

  3. anas2000
    • 2 years ago
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    your welcome

  4. glucy7
    • 2 years ago
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    wait did you like re-expand the problem after cos(5 pi/6) = -sqrt(3)/2

  5. Dwade03
    • 2 years ago
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    most of these problems are some identities written on the unit circle.

  6. glucy7
    • 2 years ago
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    okay.. well can you please explain each of the steps this person just gave me? i would reaaaalllyyyy appreciate it

  7. Dwade03
    • 2 years ago
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    ok so 5pi/12 is 75 degrees rite

  8. glucy7
    • 2 years ago
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    i guess.. lol is it?

  9. Dwade03
    • 2 years ago
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    pi is 180 degrees.lol you know that rite and u muliply tht by 5 and get 900 and divide 12 and you get 75 degrees

  10. glucy7
    • 2 years ago
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    okay but what does the 75 degrees have to do with the formula?

  11. Dwade03
    • 2 years ago
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    just to make ur question simpler... for example lets say it asked u for the cos of pi/6 which is 30 degrees.

  12. Dwade03
    • 2 years ago
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    there is some thing called the unit circle and it has this angles from 30,45,60,90 upto 360.. and since we have cos of Pi/6 which is 30 degrees. we can look at the unit circle for the cosine of 30 degrees and find it

  13. AFleming42
    • 2 years ago
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    @Dwade03 WHATS THE ANSWER?! D:

  14. AFleming42
    • 2 years ago
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    how is it done using half angle identity formula?!

  15. Dwade03
    • 2 years ago
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    ok so since they asked for cos(75) we can use the formula of using two angles to create that angle of 75. in this case we can use cos(45+35). u get tht?

  16. Lukecrayonz
    • 2 years ago
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    @ganeshie8

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