$sin\alpha=\dfrac{1}{4}$
$sin^2\alpha+cos^2\alpha=1$
$⇒cos\alpha=±\sqrt{1-sin^2\alpha}=±\sqrt{1-\bigg(\dfrac{1}{4}\bigg)^2}=±\dfrac{\sqrt{15}}{4}$
$tan\alpha=\dfrac{sin\alpha}{cos\alpha}=\dfrac{\dfrac{1}{4}}{±\dfrac{\sqrt{15}}{4}}=±\dfrac{\sqrt{15}}{16}$
$cot\alpha=\dfrac{1}{tan\alpha}=±\dfrac{16\sqrt{15}}{15}$