What is the value of cot(arcsin(6/7)) ?

The value of cot(arcsin(6/7)) is (sqrt(13))/6

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cot(arcsin(6/7))

cot (arcsin (\frac{6}{7}))

\frac{13}{6}

Decimal Notation

0.60092 \dots

Solution steps

cot (arcsin (\frac{6}{7}))

Rewrite using trig identities:

cot (arcsin (\frac{6}{7})) = \frac{1 - ( \frac{6}{7} ) ^{2}}{( \frac{6}{7} )}

Use the following identity:

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

= \frac{1 - ( \frac{6}{7} ) ^{2}}{( \frac{6}{7} )}

= \frac{1 - ( \frac{6}{7} ) ^{2}}{\frac{6}{7}}

Simplify

= \frac{13}{6}

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What is the value of cot(arcsin(6/7)) ?
The value of cot(arcsin(6/7)) is (sqrt(13))/6