For this question, I would draw it on the unit circle - and as kurt said, it's on the fourth quadrant - using ASTC. Therefore you are given the values for cos, which means you have the values of the adjacent sides and the hypotenuse.
Therefore since cos u = 2/3, you can assume the hypotenuse is 3 and the adjacent is 2.
Therefore using pythagoras' theorem, you can work out that the opposite side is rt5.
Then using your trig ratios,
sin u = rt 5 /3,
cos u = 2/3
tan u = rt 5 / 2
cot u = 2 / rt 5
However you must note the quadrant, so therefore sin, tan and cot are negative.
Therefore:
sin u = - √5 /3,
cos u = 2/3
tan u = - √5 / 2
cot u = - 2 / √5
However you must note the quadrant, so therefore sin, tan and cot are negative.
Therefore:
sin u = - √5 /3
cos u = 2/3
tan u = - √5 / 2
cot u = - 2 / √ 5
Then you just sub in the values into the required equation. (N.B. I don't undertand the 2 next to the cot, so I cheated and ignored the 2)
You should get:
(2/3 - 4/√5)
= ---------------
(√5 /2 - √5)
(2√5 - 12)
---------------
(3√5)
= ---------------
(5 - 2√5)
---------------
2
4√5 - 24
= ---------------
15√5 - 30
Correct me if I'm wrong - I could've gotten some algebra wrong when typing this because I was rushing.
