What is the value of tan(arcsin(7/25)) ?

The value of tan(arcsin(7/25)) is 7/24

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tan(arcsin(7/25))

tan (arcsin (\frac{7}{25}))

\frac{7}{24}

Decimal Notation

0.29166 \dots

Solution steps

tan (arcsin (\frac{7}{25}))

Rewrite using trig identities:

tan (arcsin (\frac{7}{25})) = \frac{( \frac{7}{25} ) 1 - ( \frac{7}{25} ) ^{2}}{1 - ( \frac{7}{25} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{7}{25} ) 1 - ( \frac{7}{25} ) ^{2}}{1 - ( \frac{7}{25} ) ^{2}}

= \frac{\frac{7}{25} 1 - ( \frac{7}{25} ) ^{2}}{1 - ( \frac{7}{25} ) ^{2}}

Simplify

= \frac{7}{24}

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