Find the Exact Value cot(arcsin(-( square root of 2)/3))

$\cot (\arcsin (- \frac{\sqrt{2}}{3}))$

Combine using the product rule for radicals.

$- \frac{\sqrt{7 \cdot 2}}{2}$

Multiply $7$ by $2$ .

$- \frac{\sqrt{14}}{2}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt{14}}{2}$

Decimal Form:

$- 1.87082869 \dots$