Consider a right triangle in which one of the angles [tex]\theta[/tex] satisfies
[tex]\sin\theta=\dfrac35\implies\theta=\sin^{-1}\dfrac35[/tex]
That is, the side opposite [tex]\theta[/tex] occurs in a ratio of 3 to 5 with the hypotenuse. The side adjacent to [tex]\theta[/tex] then occurs in a ratio of 4 to 5 with the hypotenuse. In other words,
[tex]\cos\theta=\dfrac45[/tex]
because
[tex]\sin^2\theta+\cos^2\theta=\dfrac9{25}+\dfrac{16}{25}=1[/tex]
Then in this triangle,
[tex]\cot\theta=\cot\left(\sin^{-1}\dfrac35\right)=\dfrac{\cos\theta}{\sin\theta}=\dfrac{\frac45}{\frac35}=\dfrac43[/tex]
