What is the value of cot(arcsin(-(sqrt(6))/8)) ?

The value of cot(arcsin(-(sqrt(6))/8)) is -sqrt(29/3)

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cot(arcsin(-(sqrt(6))/8))

cot (arcsin (- \frac{6}{8}))

- \frac{29}{3}

Decimal Notation

- 3.10912 \dots

Solution steps

cot (arcsin (- \frac{6}{8}))

Rewrite using trig identities:

cot (arcsin (- \frac{6}{8})) = \frac{1 - ( - \frac{6}{8} ) ^{2}}{( - \frac{6}{8} )}

Use the following identity:

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

= \frac{1 - ( - \frac{6}{8} ) ^{2}}{( - \frac{6}{8} )}

= \frac{1 - ( - \frac{6}{8} ) ^{2}}{- \frac{6}{8}}

Simplify

= - \frac{29}{3}

sec (\frac{3}{2})

arccos (sin (- \frac{5 π}{4}))

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

(sec (π))^{2}

cos (\frac{π}{20})

What is the value of cot(arcsin(-(sqrt(6))/8)) ?
The value of cot(arcsin(-(sqrt(6))/8)) is -sqrt(29/3)