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

The value of sin(arctan(1/2)) is (sqrt(5))/5

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sin(arctan(1/2))

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

\frac{5}{5}

Decimal Notation

0.4472135955

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{5}{5}

2 sin (\frac{π}{8}) cos (\frac{π}{8})

arccos (cos (- \frac{5 π}{4}))

sin (12 7^{\circ})

1 - 2 sin^{2} (\frac{π}{8})

- 2 cos (\frac{π}{3})

What is the value of sin(arctan(1/2)) ?
The value of sin(arctan(1/2)) is (sqrt(5))/5