What is the value of tan(arcsin(3/10)) ?

The value of tan(arcsin(3/10)) is (3sqrt(91))/(91)

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tan(arcsin(3/10))

tan (arcsin (\frac{3}{10}))

\frac{3 91}{91}

Decimal Notation

0.31448 \dots

Solution steps

tan (arcsin (\frac{3}{10}))

Rewrite using trig identities:

tan (arcsin (\frac{3}{10})) = \frac{( \frac{3}{10} ) 1 - ( \frac{3}{10} ) ^{2}}{1 - ( \frac{3}{10} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{3}{10} ) 1 - ( \frac{3}{10} ) ^{2}}{1 - ( \frac{3}{10} ) ^{2}}

= \frac{\frac{3}{10} 1 - ( \frac{3}{10} ) ^{2}}{1 - ( \frac{3}{10} ) ^{2}}

Simplify

= \frac{3 91}{91}

\frac{3}{cos ( 7 0 ^{\circ} )}

2 sin (\frac{3 π}{8}) cos (\frac{3 π}{8})

4 sin (5)

4 sin (3)

cos (π \frac{1}{4})

What is the value of tan(arcsin(3/10)) ?
The value of tan(arcsin(3/10)) is (3sqrt(91))/(91)