What is the value of sin(arctan(34/19)) ?

The value of sin(arctan(34/19)) is (34sqrt(1517))/(1517)

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sin(arctan(34/19))

sin (arctan (\frac{34}{19}))

\frac{34 1517}{1517}

Decimal Notation

0.87294 \dots

Solution steps

sin (arctan (\frac{34}{19}))

Rewrite using trig identities:

sin (arctan (\frac{34}{19})) = \frac{( \frac{34}{19} ) 1 + ( \frac{34}{19} ) ^{2}}{1 + ( \frac{34}{19} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{34}{19} ) 1 + ( \frac{34}{19} ) ^{2}}{1 + ( \frac{34}{19} ) ^{2}}

= \frac{\frac{34}{19} 1 + ( \frac{34}{19} ) ^{2}}{1 + ( \frac{34}{19} ) ^{2}}

Simplify

= \frac{34 1517}{1517}

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

cos (- 8) 43

\frac{30}{18.51 cos ( 3 5 ^{\circ} )}

1 - 2 sec (0)

14 [cos (\frac{π}{2}) + i sin (\frac{π}{2})]

What is the value of sin(arctan(34/19)) ?
The value of sin(arctan(34/19)) is (34sqrt(1517))/(1517)