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

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

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sin(arctan(1/(sqrt(2))))

sin (arctan (\frac{1}{2}))

\frac{3}{3}

Decimal Notation

0.57735 \dots

Solution steps

sin (arctan (\frac{1}{2}))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{3}{3}

sin (47. 3^{\circ})

arctan (\frac{10}{30})

arctan (1.333333)

7 cos (\frac{4}{3})

arctan (- 1.875)

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