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

The value of sin(arctan(-4)) is -(4sqrt(17))/(17)

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sin(arctan(-4))

sin (arctan (- 4))

- \frac{4 17}{17}

Decimal Notation

- 0.97014 \dots

Solution steps

sin (arctan (- 4))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= - \frac{4 17}{17}

sin (arctan (- 6))

sin (\frac{- 3 π}{2})

cot^{2} (0)

tan (arccos (\frac{1}{3}))

cot (0 π)

What is the value of sin(arctan(-4)) ?
The value of sin(arctan(-4)) is -(4sqrt(17))/(17)