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

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

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

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

- \frac{5}{13}

Decimal Notation

- 0.38461 \dots

Solution steps

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

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= - \frac{5}{13}

2 arctan (2) - arcsin (\frac{3}{5})

4 cos (2 (0))

arctan (\frac{20}{8})

arcsin (- \frac{8}{9})

cos (\frac{25 π}{4})

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