What is the value of sin(arctan(-2)) ?

The value of sin(arctan(-2)) is -(2sqrt(5))/5

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sin(arctan(-2))

sin (arctan (- 2))

- \frac{2 5}{5}

Decimal Notation

- 0.89442 \dots

Solution steps

sin (arctan (- 2))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= - \frac{2 5}{5}

tan (4)

sec (31 5^{\circ})

cos (4 8^{\circ})

arcsin (0.3)

sin^{2} (9 0^{\circ})

What is the value of sin(arctan(-2)) ?
The value of sin(arctan(-2)) is -(2sqrt(5))/5