If cos0= -5/13 and sin 0< 0, what is tan 0

12/5

Step-by-step explanation:

I doubt that you actually meant If cos0= -5/13 and sin 0<0.  Please use a Greek letter, such as Ф, to represent the angle.

If you'd do this, you'd have:

If cosФ= -5/13 and sin Ф<0

cos Ф and sin Ф are both negative in Quadrant III.

Recall that cos Ф = adj / hyp, and that hyp is always +.  Thus, adj = -5 and hyp = +13.  Using the Pythagorean Theorem to find opp:

opp² + adj² = hyp², or:

opp² = hyp² - adj².  Applying this, we find that opp = -12.

Recall that tan Ф = opp / adj.

Here,

tan Ф = -12 / (-5) = +12/5