What is the value of cot(arcsin(8/9)) ?

The value of cot(arcsin(8/9)) is (sqrt(17))/8

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cot(arcsin(8/9))

cot (arcsin (\frac{8}{9}))

\frac{17}{8}

Decimal Notation

0.51538 \dots

Solution steps

cot (arcsin (\frac{8}{9}))

Rewrite using trig identities:

cot (arcsin (\frac{8}{9})) = \frac{1 - ( \frac{8}{9} ) ^{2}}{( \frac{8}{9} )}

Use the following identity:

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

= \frac{1 - ( \frac{8}{9} ) ^{2}}{( \frac{8}{9} )}

= \frac{1 - ( \frac{8}{9} ) ^{2}}{\frac{8}{9}}

Simplify

= \frac{17}{8}

2 cos^{2} (\frac{π}{4}) - 1

arctan (\frac{- 4}{- 37})

arcsec (\frac{4}{3})

\frac{1}{2} arcsec (\frac{3}{2})

0.6 sec (5) (e^{5} + e^{5} tan (5))

What is the value of cot(arcsin(8/9)) ?
The value of cot(arcsin(8/9)) is (sqrt(17))/8