You can put this solution on YOUR website! There is a formula that expresses tan(2u) in terms of tan(u):
So if we can find tan(u) we can use this formula to find tan(2u).
We are given that sin(u) = -4/5. We can use one of the Pythagorean identities, , to use sin(u) to find cos(u). And once we have cos(u) we can use the fact that tan(u) = sin(u)/cos(u) to find tan(u).
Now we find the square root of each side. But which square root should we use? The positive one or the negative one? Well, since we are told that we know that u terminates in the 3rd quadrant. And in the 3rd quadrant cos is negative. So we should use the negative square root:
Now we can find tan(u):
Now we can find tan(2u):
When we divide fractions we change it to multiplying by the reciprocal:
which reduces to:
(