What is the value of sin(arctan(-1)) ?

The value of sin(arctan(-1)) is -(sqrt(2))/2

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sin(arctan(-1))

sin (arctan (- 1))

- \frac{2}{2}

Decimal Notation

- 0.70710 \dots

Solution steps

sin (arctan (- 1))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= - \frac{2}{2}

sec (- x) - sin (- x) tan (- x) = cos (x)

cos (arcsin (\frac{5}{13}))

arcsec (2)

cos (x) = \frac{2}{2}

- cos (2 π)

What is the value of sin(arctan(-1)) ?
The value of sin(arctan(-1)) is -(sqrt(2))/2