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Richard
Lv 4
Richard asked in Science & MathematicsMathematics · 1 decade ago

Exact Value sin(pi/12)sin(pi/4)?

4 Answers

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  • henry_yang67
    Lv 6
    1 decade ago
    Favorite Answer

    sin(x)sin(y)=(cos(x-y)-cos(x+y))/2

    x = pi/4

    y = pi/12

    so the answer is (cos (pi/6) - cos(pi/3))/2 = (sqrt(3)-1)/4

  • Pauley Morph
    Lv 7
    1 decade ago

    This is Henry's answer from a different point of view.

    cos(π/3) = cos(π/4 + π/12) = cos(π/4) cos(π/12) - sin(π/4) sin(π/12)

    cos(π/6) = cos(π/4 - π/12) = cos(π/4) cos(π/12) + sin(π/4) sin(π/12)

    sin(π/4) sin(π/12) = (cos(π/6) - cos(π/3))/2

    sin(π/4) sin(π/12) = (√3/2 - 1/2)/2 = (√3 - 1)/4

  • ?
    Lv 6
    1 decade ago

    sin(pi/12)=(root6-root2)/4 sin(pi/4)=1/root2 so anwer is (root3-1)/4

  • Elizabeth M
    Lv 7
    1 decade ago

    Use the relation 2sinAsinB=cos(A-B) - cos(A+B) and you will get (sqrt(3)-1)/2

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