precal

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use the half angle formula to determine the exact values of sin, cos, and tan of the angle.

pie/8

and

pie/12

  • precal -

    I will be happy to check your thinking on this.

  • precal -

    i honestly don't know what to do or how to start anyways

  • precal -

    the half-angle formulas let you split an angle in half
    there is sin 2A = 2sinAcosA and
    cos 2A = cos^2 A - sin^2 A or
    cos 2A = 2cos^2 A - 1 or
    cos 2A = 1 - 2sin^2 A

    I will do the pi/12 angle for you.

    pi/6 rads = 30 degrees, and pi/12 = 15 degrees
    From the 30-60-90 triangle you should know
    sin30 = 1/2 and cos30 = ?3/2

    cos 30 = 1 - 2sin^2 15
    2sin^2 15 = 1-?3/2
    sin ^2 15 = 1/2 - ?3/4
    = (2-?3)4
    so sin 15 = ?(2-?3)/2
    or sin pi/12 = ?(2-?3)/2

    now ;use the other version of cos 2A to get cos pi/12
    and since tanx = sinx/cosx, divide the two results to get the tangent.

    verify your answer with your calculator

    for the first pi/8 is half of pi/4 which is 45 degrees
    you should know the trig rations for 45 degrees.

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