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

The value of tan(arcsin(7/9)) is (7sqrt(2))/8

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tan(arcsin(7/9))

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

\frac{7 2}{8}

Decimal Notation

1.23743 \dots

Solution steps

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

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{7 2}{8}

- 8 sin (\frac{π}{4})

2 sin (1 0^{\circ})

7 cos (3 5^{\circ})

4 sin (- \frac{π}{4})

3 cos (\frac{7 π}{4})

What is the value of tan(arcsin(7/9)) ?
The value of tan(arcsin(7/9)) is (7sqrt(2))/8