Question 850183
cos is adjacent/hypotenuse.  So the adjacent side to the angle (one of the legs) is 5. Since this is quadrant II, it's -5.  The hypotenuse is 13.  You can find the other leg (opposite side) using the Pythagorean theorem {{{a^2 + b^2 = h^2}}} where a and b are legs and h is the hypotenuse.  This can be rearranged as {{{a^2 = h^2 - b^2 = 13^2 - (-5)^2 = 169-25 = 144.<P>
a = sqrt(144) = 12.  Since the angle is in quadrant II, 12 is positive, because sin is positive in quadrant II.  Only the 5 is negative.<P>
Tan is opposite/adjacent = 12/(-5) = -12/5.<P>
Now use the double angle formula:  {{{tan2x = 2tanx / 1 - tan^2(x)}}}<P>
{{{tan2c = 2*(-12/5) / (1-(-12/5)^2)}}}<P>
tan2c = -24/5 / (1-144/25) = -24/5 / (-119/25) = -24/5 * -25/119 = 120/119 = approximately 1.008