What is the value of cot(arcsin(7/9)) ?

The value of cot(arcsin(7/9)) is (4sqrt(2))/7

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cot(arcsin(7/9))

cot (arcsin (\frac{7}{9}))

\frac{4 2}{7}

Decimal Notation

0.80812 \dots

Solution steps

cot (arcsin (\frac{7}{9}))

Rewrite using trig identities:

cot (arcsin (\frac{7}{9})) = \frac{1 - ( \frac{7}{9} ) ^{2}}{( \frac{7}{9} )}

Use the following identity:

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

= \frac{1 - ( \frac{7}{9} ) ^{2}}{( \frac{7}{9} )}

= \frac{1 - ( \frac{7}{9} ) ^{2}}{\frac{7}{9}}

Simplify

= \frac{4 2}{7}

4 sin (2 \cdot \frac{π}{6})

cos (π (- 1))

sin (4 5^{\circ}) - sin (3 0^{\circ})

160 cos (20 0^{\circ})

cot (\frac{π}{4}) - \frac{π}{4} csc^{2} (\frac{π}{4})

What is the value of cot(arcsin(7/9)) ?
The value of cot(arcsin(7/9)) is (4sqrt(2))/7