What is the value of tan(arcsin(1/3)) ?

The value of tan(arcsin(1/3)) is (sqrt(2))/4

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tan(arcsin(1/3))

tan (arcsin (\frac{1}{3}))

\frac{2}{4}

Decimal Notation

0.35355 \dots

Solution steps

tan (arcsin (\frac{1}{3}))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{2}{4}

\frac{sin ( 0.1 )}{0.1}

cos (7 4^{\circ})

arctan (\frac{7}{3})

arctan (\frac{7}{5})

sin (2 0^{\circ}) cos (4 0^{\circ}) + cos (2 0^{\circ}) sin (4 0^{\circ})

What is the value of tan(arcsin(1/3)) ?
The value of tan(arcsin(1/3)) is (sqrt(2))/4