What is the value of cot(arcsin(-(sqrt(2))/8)) ?

The value of cot(arcsin(-(sqrt(2))/8)) is -sqrt(31)

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cot(arcsin(-(sqrt(2))/8))

cot (arcsin (- \frac{2}{8}))

- 31

Decimal Notation

- 5.56776 \dots

Solution steps

cot (arcsin (- \frac{2}{8}))

Rewrite using trig identities:

cot (arcsin (- \frac{2}{8})) = \frac{1 - ( - \frac{2}{8} ) ^{2}}{( - \frac{2}{8} )}

Use the following identity:

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

= \frac{1 - ( - \frac{2}{8} ) ^{2}}{( - \frac{2}{8} )}

= \frac{1 - ( - \frac{2}{8} ) ^{2}}{- \frac{2}{8}}

Simplify

= - 31

47 cos (10 8^{\circ})

arcsinh (4)

cos (1 0^{\circ}) cos (3 5^{\circ}) - sin (1 0^{\circ}) sin (3 5^{\circ})

cos^{2} (3 2^{\circ})

- e^{- 0} cos (0) - e^{- 0} sin (0)

What is the value of cot(arcsin(-(sqrt(2))/8)) ?
The value of cot(arcsin(-(sqrt(2))/8)) is -sqrt(31)