Trig

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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?

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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 don't 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!

  • Trig -

    You have not attempted the first question. You know that 2x is between 270 and 360 degrees. That means x must be in the second quadrant, between 135 and 180 degrees.

    In part 2, for cos x, use the formula
    cos 2x = 8/17 = 2cos^2x -1
    and solve for cos x. You first find out what cos^2 x is. Since x is in the second quadrant, cos x will be negative. You do NOT divide numerator and denominator of cos 2x by 2. That would leave you with the same number.

    2 cos^2x = 25/17
    cos^2x = 25/34
    cosx = -0.85749

    Once you have a number for cosx, and realize it is negative, take the inverse cosine and convert it to radians in the usual way.

  • Trig -

    if cos 2x is 8/17, then...

    Use cos(2x)=2cos^2 x -1 identity to find cos x. What quadrant? If 2x is in quadrant IV, then x has to be in quadrant II.

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