Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 weeks ago

How do I use a half-angle formula to find the exact value of 5π/12?

Update:

It's supposed to be sin 5π/12 and I am so sorry for that mistake

5 Answers

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  • 2 weeks ago
    Best Answer

    We use the identity   sin^2 (x) =  ( 1 - cos(2x))/2 

    Since sin^2 (5π/12) = ( 1 - cos(2 * 5π/12 ) / 2 

      = (  1 - cos(5π/6) / 2 

    =  (  1 - cos( π - π / 6))/2

    =  ( 1 - ( - cos(π /6) )/2

    =  ( 1 +  √3 / 2 ) / 2

    =    ( 1/2 +  √3 / 4)

    So sin( 5π/12) = √ ( 1/2 + √3 / 4)   

       we reject -ve value since we are in first quadrant

    We can now get cos (  5π/12 )  using  sin^2 u + cos^2 u = 1

    then we can get  tan(5π/12) ( = sin(5π/12) / cos( 5π/12 ) ) 

  • 2 weeks ago

    The exact value of 5π /12 is (5/12) pi. Are you looking for the sine, cosine, and tangent of that angle?

  • sin(5pi/12) = 

    sin((5pi/6)/2) = 

    sqrt((1/2) * (1 - cos(5pi/6)))cos(5pi/12) = cos((5pi/6)/2) = sqrt((1/2) * (1 + cos(5pi/6)))tan(5pi/12) = sin(5pi/12)/cos(5pi/12) =

    sqrt((1/2) * (1 - cos(5pi/6))) / sqrt((1/2) * (1 + cos(5pi/6))) =

    sqrt((1 - cos(5pi/6)) / (1 + cos(5pi/6))) =

    sqrt((1 - cos(5pi/6))^2 / (1 - cos(5pi/6)^2)) =

    (1 - cos(5pi/6)) / sqrt(sin(5pi/6))^2) =

    (1 - cos(5pi/6)) / sin(5pi/6)

    csc(5pi/12) = 1/sin(5pi/12)

    sec(5pi/12) = 1/cos(5pi/12)

    cot(5pi/12) = sin(5pi/6) / (1 - cos(5pi/6))

  • David
    Lv 7
    2 weeks ago

    You never will because pi is an irrational number.

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  • Jay
    Lv 6
    2 weeks ago

    by applying the formula to figure out the value

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