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