#1**+1 **

If you place this angle on a rectangular grid

-- cos(x) < 0 means that the terminal side of theangle must be in either quadrant II or quadrant III

-- tan(x) > 0 means that the terminal side of theangle must be in either quadrant I or quadrant III.

Therefore, the terminal side of the angle is in quadrant III.

Since tan(x) = 4, the point in quadrant III can be (-1, -4).

This means that the radius is sqrt( (-1)^{2} + (-4)^{2} ) = sqrt(17).

Therefore, sin(x) = -4/sqrt(17) and cos(x) = -1/sqrt(17).

You can use the formula: sin(2x) = 2·sin(x)·cos(x)

and any of the formulas for cos(2x); one of them being cos(2x) = 1 - sin^{2}(x).

geno3141 Apr 22, 2020