What is the value of sin(arctan(2/5)) ?

The value of sin(arctan(2/5)) is (2sqrt(29))/(29)

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sin(arctan(2/5))

sin (arctan (\frac{2}{5}))

\frac{2 29}{29}

Decimal Notation

0.37139 \dots

Solution steps

sin (arctan (\frac{2}{5}))

Rewrite using trig identities:

sin (arctan (\frac{2}{5})) = \frac{( \frac{2}{5} ) 1 + ( \frac{2}{5} ) ^{2}}{1 + ( \frac{2}{5} ) ^{2}}

Use the following identity:

sin (arctan (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 29}{29}

\frac{sin ( 6 0 ^{\circ} ) \cdot tan ( 3 0 ^{\circ} )}{sec ( 4 5 ^{\circ} )}

- 4 π^{2} cos (π + \frac{π}{4})

sin (\frac{13}{12} π)

22 cos (4 5^{\circ})

sinh^{2} (1)

What is the value of sin(arctan(2/5)) ?
The value of sin(arctan(2/5)) is (2sqrt(29))/(29)