If sec α = -5/3 and α has its terminal side in quadrant II, find the exact value of tan 2α

Answer 1

If the secant angle is -5/3 in the second quadrant is, it turns out be a 3-4-5 right triangle with the reference angle of 53.1° from the x-axis or the actual angle of 126.9 degrees. So at this point you can use the trig identity for the double angle which is 2*tangent of the angle divided by (1 - tangent squared of the angle). Or you can actually just take the tangent of 2×126.9 which is the tangent of 253.8 degrees which is 3.44. I checked it by using the double angle formula and I got 24/7. So I suggest the answer is 3.44.