What is the value of sin(arctan((-4)/3)) ?

The value of sin(arctan((-4)/3)) is -4/5

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sin(arctan((-4)/3))

sin (arctan (\frac{- 4}{3}))

- \frac{4}{5}

Decimal Notation

- 0.8

Solution steps

sin (arctan (\frac{- 4}{3}))

Rewrite using trig identities:

sin (arctan (\frac{- 4}{3})) = \frac{( \frac{- 4}{3} ) 1 + ( \frac{- 4}{3} ) ^{2}}{1 + ( \frac{- 4}{3} ) ^{2}}

Use the following identity:

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

= \frac{( \frac{- 4}{3} ) 1 + ( \frac{- 4}{3} ) ^{2}}{1 + ( \frac{- 4}{3} ) ^{2}}

= \frac{\frac{- 4}{3} 1 + ( \frac{- 4}{3} ) ^{2}}{1 + ( \frac{- 4}{3} ) ^{2}}

Simplify

= - \frac{4}{5}

tan (3 0^{\circ}) cot (3 0^{\circ}) + cos (36 0^{\circ}) sin (15 0^{\circ})

\frac{2 cos ^{2} ( 4 5 ^{\circ} ) - 1}{tan ( 4 5 ^{\circ} )}

40 \cdot cos (2 0^{\circ})

sin (4 5^{\circ}) 3

2 sin (\frac{π}{2})

What is the value of sin(arctan((-4)/3)) ?
The value of sin(arctan((-4)/3)) is -4/5