What is the value of cot(arcsin(-(sqrt(5))/6)) ?

The value of cot(arcsin(-(sqrt(5))/6)) is -sqrt(31/5)

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cot(arcsin(-(sqrt(5))/6))

cot (arcsin (- \frac{5}{6}))

- \frac{31}{5}

Decimal Notation

- 2.48997 \dots

Solution steps

cot (arcsin (- \frac{5}{6}))

Rewrite using trig identities:

cot (arcsin (- \frac{5}{6})) = \frac{1 - ( - \frac{5}{6} ) ^{2}}{( - \frac{5}{6} )}

Use the following identity:

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

= \frac{1 - ( - \frac{5}{6} ) ^{2}}{( - \frac{5}{6} )}

= \frac{1 - ( - \frac{5}{6} ) ^{2}}{- \frac{5}{6}}

Simplify

= - \frac{31}{5}

e^{- 0} cos (0)

cos^{2} (6 5^{\circ})

tan^{3} (0)

cos^{2} (14 0^{\circ})

sin (32 0^{\circ})

What is the value of cot(arcsin(-(sqrt(5))/6)) ?
The value of cot(arcsin(-(sqrt(5))/6)) is -sqrt(31/5)