2x, given tanx=4 and cosx<0 what is cos2x and sin2x
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 - sin2(x).