What is the value of sin(arctan((-12)/5)) ?

The value of sin(arctan((-12)/5)) is -12/13

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sin(arctan((-12)/5))

sin (arctan (\frac{- 12}{5}))

- \frac{12}{13}

Decimal Notation

- 0.92307 \dots

Solution steps

sin (arctan (\frac{- 12}{5}))

Rewrite using trig identities:

sin (arctan (\frac{- 12}{5})) = \frac{( \frac{- 12}{5} ) 1 + ( \frac{- 12}{5} ) ^{2}}{1 + ( \frac{- 12}{5} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{- 12}{5} ) 1 + ( \frac{- 12}{5} ) ^{2}}{1 + ( \frac{- 12}{5} ) ^{2}}

= \frac{\frac{- 12}{5} 1 + ( \frac{- 12}{5} ) ^{2}}{1 + ( \frac{- 12}{5} ) ^{2}}

Simplify

= - \frac{12}{13}

2 sin (0) cos (0)

\frac{tan ( 4 5 ^{\circ} )}{cos ( 4 5 ^{\circ} )}

arctan (1) - arctan (2)

\frac{1}{2} arcsin (- 1)

4 cos (2 \cdot \frac{π}{6})

What is the value of sin(arctan((-12)/5)) ?
The value of sin(arctan((-12)/5)) is -12/13