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.
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!
2 answers
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.
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.
2 answers