What is the value of cot(arcsin(-2/5)) ?

The value of cot(arcsin(-2/5)) is -(sqrt(21))/2

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cot(arcsin(-2/5))

cot (arcsin (- \frac{2}{5}))

- \frac{21}{2}

Decimal Notation

- 2.29128 \dots

Solution steps

cot (arcsin (- \frac{2}{5}))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= - \frac{21}{2}

\frac{1}{cos ( 0 )}

arctan (\frac{2}{6})

tan (\frac{- π}{4})

arccos (0.3)

sin (\frac{4 π}{5})

What is the value of cot(arcsin(-2/5)) ?
The value of cot(arcsin(-2/5)) is -(sqrt(21))/2