Are these correct?

Question

5. is sin θ = -7/13 and cos θ = 12/13, find tan θ and cot θ using Quotient Identities.

answers:
tan (θ) = -(7/12)
cot (θ) = -(12/7)

Answer 1

I was looking to recognize the 5-12-13 right-angled triangle ratio
but saw sin θ = -7/13 instead of the expected sin θ = -5/13
( 7^2 + 12^2 ≠ 13^2 , but 5^2 + 12^2 = 13^2 )

So I will assume you have a typo.
The sine is negative and the cosine is positive only in Quadrant IV
so in that quad construct the right-angled triangle
Clearly: x = 12, y = -5 and r = 13
so tan θ = y/x = -5/12
and cot θ = -12/5