What is the value of sin(arctan(3/8)) ?

The value of sin(arctan(3/8)) is (3sqrt(73))/(73)

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sin(arctan(3/8))

sin (arctan (\frac{3}{8}))

\frac{3 73}{73}

Decimal Notation

0.35112 \dots

Solution steps

sin (arctan (\frac{3}{8}))

Rewrite using trig identities:

sin (arctan (\frac{3}{8})) = \frac{( \frac{3}{8} ) 1 + ( \frac{3}{8} ) ^{2}}{1 + ( \frac{3}{8} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{3}{8} ) 1 + ( \frac{3}{8} ) ^{2}}{1 + ( \frac{3}{8} ) ^{2}}

= \frac{\frac{3}{8} 1 + ( \frac{3}{8} ) ^{2}}{1 + ( \frac{3}{8} ) ^{2}}

Simplify

= \frac{3 73}{73}

- 0.208 + (\frac{5}{4} sin^{2} (0.5) - \frac{5}{12}) 0.5

cos (4 \cdot \frac{π}{2})

35 \cdot cos (6 0^{\circ})

2 sec^{2} (\frac{π}{6})

\frac{4 ( 4 + sin ( 4 ) )}{3}

What is the value of sin(arctan(3/8)) ?
The value of sin(arctan(3/8)) is (3sqrt(73))/(73)