If cos x=−6/7, and 90°<x<180°, what is cos⁡(2x)?

Question

If cos x=−6/7, and 90°<x<180°, what is cos⁡(2x)?

Answer 1

Hi Alice,

Since cos x=−6/7 (negative) and 90°<x<180°, then angle x must be in the second quadrant. Note also that 2x is between 180 and 360.

Now for the formula: cos(2x) = 2* cos^2(x) - 1 = 2*(-6/7)^2 -1 = 2*(36/49) - 1 = 0.469 which is positive. This indicates that angle 2x is in the fourth quadrant.

Robert