What is the value of tan(arcsin(4/7)) ?

The value of tan(arcsin(4/7)) is (4sqrt(33))/(33)

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tan(arcsin(4/7))

tan (arcsin (\frac{4}{7}))

\frac{4 33}{33}

Decimal Notation

0.69631 \dots

Solution steps

tan (arcsin (\frac{4}{7}))

Rewrite using trig identities:

tan (arcsin (\frac{4}{7})) = \frac{( \frac{4}{7} ) 1 - ( \frac{4}{7} ) ^{2}}{1 - ( \frac{4}{7} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{4}{7} ) 1 - ( \frac{4}{7} ) ^{2}}{1 - ( \frac{4}{7} ) ^{2}}

= \frac{\frac{4}{7} 1 - ( \frac{4}{7} ) ^{2}}{1 - ( \frac{4}{7} ) ^{2}}

Simplify

= \frac{4 33}{33}

tan (\frac{π}{4} + \frac{π}{6})

arccos (\frac{2}{20})

2.5 sin (9 0^{\circ})

3.5 sin (1 6^{\circ})

cot (0^{+})

What is the value of tan(arcsin(4/7)) ?
The value of tan(arcsin(4/7)) is (4sqrt(33))/(33)