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Kool Kid on the block
Kool Kid on the block asked in Science & MathematicsMathematics · 3 years ago

HELP WITH TRIG HW: Half angle formulas?

Is my answer correct? Any help is appreciated!

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3 Answers

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  • DWRead
    Lv 7
    3 years ago
    Favorite Answer

    Looks good to me.

     

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  • lenpol7
    Lv 7
    3 years ago

    67.5 = 90 - 22.5 = pi/2 - pi/8

    Hence

    Sin(67.5) = Sin(90 - 22.5) = Sin(pi/2 - pi/8)

    Using the Trig identity

    Sin(pi/2)Cos(pi/8) - Cos(pi/2)(Sin(pi/8) =>

    Cos(pi/8) - 0

    Cos(pi/8) =

    Cos( 3.141592... / 8) =cos(0/3926999...) = 0.9238....

  • Anonymous
    3 years ago

    let 67.5 = x

    x = y/2 => y = 135

    sin(x) = sin(y/2) = +/-√((1 - cos(y))/2)

    x is in the first quadrant, so take positive root

    sin(y/2) = √((1 - cos(y))/2)

    let z = 2y => z = 270

    cos(y) = cos(z/2) = +/-√((1 + cos(z))/2)

    y is in second quadrant, so take negative root

    cos(z/2) = -√((1 + cos(z))/2)

    cos(270) = 0

    so cos(y) = -√(1/2)

    so sin(x) = √((1 + √(1/2))/2)

    sin(x) = √(2 + √2)/2

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