Evaluate Cot0 if sin0 = square root of 6/5

To evaluate cot θ given that sinθ=√6/5 we shall have:

sin θ=opposite/hypotenuse

hence

opposite=√6

hypotenuse=5

thus the adjacent will be found using the Pythagorean theorem

c²=a²+b²

plugging in the value we get:

5² = (√6) ²+b²

b²=25-6

b²=19

b=√19

thus

adjacent=√19

but

cotθ=1/tanθ

tanθ=√6/√19

hence:

cotθ=√19/√6