What is the value of sin(arctan(2/3)) ?

The value of sin(arctan(2/3)) is (2sqrt(13))/(13)

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sin(arctan(2/3))

sin (arctan (\frac{2}{3}))

\frac{2 13}{13}

Decimal Notation

0.55470 \dots

Solution steps

sin (arctan (\frac{2}{3}))

Rewrite using trig identities:

sin (arctan (\frac{2}{3})) = \frac{( \frac{2}{3} ) 1 + ( \frac{2}{3} ) ^{2}}{1 + ( \frac{2}{3} ) ^{2}}

Use the following identity:

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

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

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

Simplify

= \frac{2 13}{13}

- 1 - 2 arctan (- 1)

\frac{8}{sin ( 3 0 ^{\circ} )}

tan (arcsin (\frac{- 3}{4}))

cos (3 0^{\circ}) + sin (3 0^{\circ})

arctan (32)

What is the value of sin(arctan(2/3)) ?
The value of sin(arctan(2/3)) is (2sqrt(13))/(13)