Draw a right triangle in quadrant IV,
indicate the reference angle (the one inside the
triangle with one side as the x-axis) with an
arc:



Since ,
label the opposite side to the reference angle as the numerator
of -7/6  which is -7 (negative since the opposite side goes
down) and the adjacent side as +6 (positive since it goes
right.



Find the hypotenuse by the Pythagorean theorem:







We always take the hypotenuse as positive in trigonometry.
Label it 



Now we just plug in the formulas for sin(2x), cos(2x), and tan(2x),
using opposite, adjacent, and hypotenuse to find the trig ratios
for x.










Edwin