cos theta=2/3 and tan theta is less then 0

Question

I need the sin, csc, sec, cos, tan, and cot

Answer 1

I believe you mean tan θ is less than 0, which information tells you that theta is in quadrant IV.

 

Using the Pythagorean identity, you can then calculate the sine, given the cosine value.  The rest is THEN straightforward.