What is the value of cot(arcsin(-(sqrt(2))/3)) ?

The value of cot(arcsin(-(sqrt(2))/3)) is -sqrt(7/2)

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cot(arcsin(-(sqrt(2))/3))

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

- \frac{7}{2}

Decimal Notation

- 1.87082 \dots

Solution steps

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

Rewrite using trig identities:

cot (arcsin (- \frac{2}{3})) = \frac{1 - ( - \frac{2}{3} ) ^{2}}{( - \frac{2}{3} )}

Use the following identity:

cot (arcsin (x)) = \frac{1 - x ^{2}}{x}

= \frac{1 - ( - \frac{2}{3} ) ^{2}}{( - \frac{2}{3} )}

= \frac{1 - ( - \frac{2}{3} ) ^{2}}{- \frac{2}{3}}

Simplify

= - \frac{7}{2}

cot (5 0^{\circ})

arctan (\frac{3}{- 3})

1 + cos (0)

sin (\frac{π}{1})

cos (arccos (1.2))

What is the value of cot(arcsin(-(sqrt(2))/3)) ?
The value of cot(arcsin(-(sqrt(2))/3)) is -sqrt(7/2)