What is the value of sin(arctan(3/5)) ?

The value of sin(arctan(3/5)) is (3sqrt(34))/(34)

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sin(arctan(3/5))

sin (arctan (\frac{3}{5}))

\frac{3 34}{34}

Decimal Notation

0.51449 \dots

Solution steps

sin (arctan (\frac{3}{5}))

Rewrite using trig identities:

sin (arctan (\frac{3}{5})) = \frac{( \frac{3}{5} ) 1 + ( \frac{3}{5} ) ^{2}}{1 + ( \frac{3}{5} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{3}{5} ) 1 + ( \frac{3}{5} ) ^{2}}{1 + ( \frac{3}{5} ) ^{2}}

= \frac{\frac{3}{5} 1 + ( \frac{3}{5} ) ^{2}}{1 + ( \frac{3}{5} ) ^{2}}

Simplify

= \frac{3 34}{34}

sec (\frac{14 π}{3})

csc (arcsec (- 2))

\frac{cos ( 6 0 ^{\circ} )}{cos ( 6 0 ^{\circ} )}

arccos (\frac{- 58}{129 53})

arctan (\frac{21}{28})

What is the value of sin(arctan(3/5)) ?
The value of sin(arctan(3/5)) is (3sqrt(34))/(34)