If cos a = 3/5 in the first quadrant, what does cot a equal

Given that cos a = 3/5 and it is in the first quadrant:

then:

a=arccos 3/5

but

cot θ=1/tan θ

thus to evaluate our vale we shall obtain the value for height since

adjacent=3

hypotenuse=5

thus

using Pythagorean theorem:

c²=a²+b²

hence

5²=3²+b²

b²=25-9=16

b=4

thus

tan θ=opposite/adjacent

tan a=4/3

thus

cot a=1 / (4/3) = 3/4