What is the value of cot(arcsin(-(sqrt(3))/5)) ?

The value of cot(arcsin(-(sqrt(3))/5)) is -sqrt(22/3)

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cot(arcsin(-(sqrt(3))/5))

cot (arcsin (- \frac{3}{5}))

- \frac{22}{3}

Decimal Notation

- 2.70801 \dots

Solution steps

cot (arcsin (- \frac{3}{5}))

Rewrite using trig identities:

cot (arcsin (- \frac{3}{5})) = \frac{1 - ( - \frac{3}{5} ) ^{2}}{( - \frac{3}{5} )}

Use the following identity:

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

= \frac{1 - ( - \frac{3}{5} ) ^{2}}{( - \frac{3}{5} )}

= \frac{1 - ( - \frac{3}{5} ) ^{2}}{- \frac{3}{5}}

Simplify

= - \frac{22}{3}

arcsin (\frac{1}{10})

cos (1) + \frac{ln ( 1 )}{2}

sin (\frac{π}{4} + \frac{π}{2})

2 cos^{2} (4 0^{\circ}) - 1

15 sin (\frac{π}{3})

What is the value of cot(arcsin(-(sqrt(3))/5)) ?
The value of cot(arcsin(-(sqrt(3))/5)) is -sqrt(22/3)