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

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

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sin(arctan(3/2))

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

\frac{3 13}{13}

Decimal Notation

0.83205 \dots

Solution steps

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

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{3 13}{13}

2 (cos (\frac{π}{3}) + i sin (\frac{π}{3}))

tan (33.6 9^{\circ})

\frac{tan ( 6 0 ^{\circ} ) sin ( 3 0 ^{\circ} )}{cos ( 6 0 ^{\circ} )}

- sin (\frac{7 π}{2})

\frac{1 - cos ( - 0.1 )}{- 0.1}

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