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}

arctan (\frac{( - 3 )}{3})

\frac{60}{cos ( 3 0 ^{\circ} )}

cos (- 58 5^{\circ})

cos (- 1 (- 1))

cos (- 40 5^{\circ})

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