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

The value of sin(arctan(-3)) is -(3sqrt(10))/(10)

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sin(arctan(-3))

sin (arctan (- 3))

- \frac{3 10}{10}

Decimal Notation

- 0.94868 \dots

Solution steps

sin (arctan (- 3))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= - \frac{3 10}{10}

sin (\frac{5}{13})

arctan (tan (\frac{4 π}{5}))

arccos (cos (\frac{15 π}{4}))

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

cos (0.6)

What is the value of sin(arctan(-3)) ?
The value of sin(arctan(-3)) is -(3sqrt(10))/(10)