Answer:
cot∅ = (-2√30)/7.
Explanation:
Given the value of csc∅ = -13/7 and ∅ is in quad III.
We know y = r sin∅ and r > 0. So csc∅ = r/y = -13/7 = 13/(-7).
It means y = -7, r = 13.
We know x² + y² = r².
x² = r² - y²
x² = (13)² - (-7)² = 169 - 49 = 120.
x = √120 = 2√30.
we know cot∅ = x/y = (2√30)/(-7) = (-2√30)/7.
Hence, cot∅ = (-2√30)/7.