Answer
(a) $tan~\alpha=\frac{1}{3}$
(b) $csc~\alpha=\sqrt {10}$
(c) $cot(90°-\alpha)=\frac{1}{3}$
(d) $sin~\alpha=\frac{\sqrt {10}}{10}$
Work Step by Step
(a) $tan~\alpha=\frac{1}{cot~\alpha}=\frac{1}{3}$
(b)
$csc^2\alpha=cot^2\alpha+1=3^2+1=10$
$csc~\alpha=\sqrt {10}$
(c) $cot(90°-\alpha)=tan~\alpha=\frac{1}{3}$
(d) $sin~\alpha=\frac{1}{csc~\alpha}=\frac{1}{\sqrt {10}}=\frac{\sqrt {10}}{10}$
