Answer
$csc~18^{\circ} = \sqrt{5}+1$
Work Step by Step
$csc~x = \frac{1}{sin~x}$
We can find the value of $csc~18^{\circ}$:
$csc~18^{\circ} = \frac{1}{sin~18^{\circ}}$
$csc~18^{\circ} = \frac{1}{\frac{\sqrt{5}-1}{4}}$
$csc~18^{\circ} = \frac{4}{\sqrt{5}-1}$
$csc~18^{\circ} = \frac{4}{\sqrt{5}-1}~\frac{\sqrt{5}+1}{\sqrt{5}+1}$
$csc~18^{\circ} = \frac{4~(\sqrt{5}+1)}{4}$
$csc~18^{\circ} = \sqrt{5}+1$
