Question

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

Answer 1

12/5

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