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

The value of sin(arctan((sqrt(3))/3)) is 1/2

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sin(arctan((sqrt(3))/3))

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

\frac{1}{2}

Decimal Notation

0.5

Solution steps

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

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{1}{2}

25 sin (3 0^{\circ})

arcsin (\frac{- 1}{2})

3 π + sin^{2} (\frac{3 π}{3}) - 8

arccos (0.87)

arccos (0.28)

What is the value of sin(arctan((sqrt(3))/3)) ?
The value of sin(arctan((sqrt(3))/3)) is 1/2