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Math Help - Double Angle Forumla

  1. #1
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    Double Angle Forumla

    The angle 2x lies in the fourth quadrant such that cos2x=8/17.

    1.Which quadrant contains angle x?
    2. Determine an exact value for cosx
    3. What is the measure of x in radians?

    ----------------
    I know that quadrant 4 has 2x in it, so quadrant _____ has to have x ?
    for part 2, the exact measure of cosx would, it be 4/8.5??? I divided 8 by two and 17 by two.. I dont know if it is right. Check?

    For part 3, the measure of x, would I have to take cos^-1(4/8.5) [ if part b is right] to get the measure of x? Thanks!
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  2. #2
    Super Member craig's Avatar
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    Quote Originally Posted by skeske1234 View Post
    2. Determine an exact value for cosx
    for part 2, the exact measure of cosx would, it be 4/8.5??? I divided 8 by two and 17 by two.. I dont know if it is right. Check?
    No, \cos{2x} is not the same as 2\cos{x}

    The double angle formula states that \cos{2x} = 2\cos^2{x} - 1.

    Therefore 2\cos^2{x} - 1 = \frac{8}{17} , can you work this one out now?


    Quote Originally Posted by skeske1234 View Post
    For part 3, the measure of x, would I have to take cos^-1(4/8.5) [ if part b is right] to get the measure of x?
    No I'm afraid this is incorrect.

    Let me give you an example, if \cos{nx} = q for example where n and q are just numbers, then nx = \cos^{-1}{q}, therefore x = \frac{\cos^{-1}{q}}{n}.

    Can you work this one through?
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  3. #3
    Super Member craig's Avatar
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    As for the first part I'm afraid I'm unsure about the quadrant method.
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