What is the value of tan(arcsin(2/5)) ?

The value of tan(arcsin(2/5)) is (2sqrt(21))/(21)

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tan(arcsin(2/5))

tan (arcsin (\frac{2}{5}))

\frac{2 21}{21}

Decimal Notation

0.43643 \dots

Solution steps

tan (arcsin (\frac{2}{5}))

Rewrite using trig identities:

tan (arcsin (\frac{2}{5})) = \frac{( \frac{2}{5} ) 1 - ( \frac{2}{5} ) ^{2}}{1 - ( \frac{2}{5} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{2}{5} ) 1 - ( \frac{2}{5} ) ^{2}}{1 - ( \frac{2}{5} ) ^{2}}

= \frac{\frac{2}{5} 1 - ( \frac{2}{5} ) ^{2}}{1 - ( \frac{2}{5} ) ^{2}}

Simplify

= \frac{2 21}{21}

2 tan (6 0^{\circ})

sin (2 arccos (- \frac{2}{2}))

sin (\frac{3}{8})

sin (\frac{\frac{2 π}{3}}{2})

arcsin (\frac{9}{14})

What is the value of tan(arcsin(2/5)) ?
The value of tan(arcsin(2/5)) is (2sqrt(21))/(21)