What is the value of cot(arcsin(-(sqrt(5))/7)) ?

The value of cot(arcsin(-(sqrt(5))/7)) is -(2sqrt(55))/5

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cot(arcsin(-(sqrt(5))/7))

cot (arcsin (- \frac{5}{7}))

- \frac{2 55}{5}

Decimal Notation

- 2.96647 \dots

Solution steps

cot (arcsin (- \frac{5}{7}))

Rewrite using trig identities:

cot (arcsin (- \frac{5}{7})) = \frac{1 - ( - \frac{5}{7} ) ^{2}}{( - \frac{5}{7} )}

Use the following identity:

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

= \frac{1 - ( - \frac{5}{7} ) ^{2}}{( - \frac{5}{7} )}

= \frac{1 - ( - \frac{5}{7} ) ^{2}}{- \frac{5}{7}}

Simplify

= - \frac{2 55}{5}

30 cos (9 0^{\circ})

cos (arctan (\frac{5}{7}) - arctan (\frac{1}{6}))

sin (arccos (- \frac{5}{6}))

\frac{tan ( \frac{π}{3} ) + tan ( \frac{π}{4} )}{1 - tan ( \frac{π}{3} ) tan ( \frac{π}{4} )}

cos (9 0^{\circ} + 24 0^{\circ})

What is the value of cot(arcsin(-(sqrt(5))/7)) ?
The value of cot(arcsin(-(sqrt(5))/7)) is -(2sqrt(55))/5