What is the value of sin(arctan(-12/5)) ?

The value of sin(arctan(-12/5)) is -12/13

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sin(arctan(-12/5))

sin (arctan (- \frac{12}{5}))

- \frac{12}{13}

Decimal Notation

- 0.92307 \dots

Solution steps

sin (arctan (- \frac{12}{5}))

Rewrite using trig identities:

sin (arctan (- \frac{12}{5})) = \frac{( - \frac{12}{5} ) 1 + ( - \frac{12}{5} ) ^{2}}{1 + ( - \frac{12}{5} ) ^{2}}

Use the following identity:

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

= \frac{( - \frac{12}{5} ) 1 + ( - \frac{12}{5} ) ^{2}}{1 + ( - \frac{12}{5} ) ^{2}}

= \frac{( - \frac{12}{5} ) 1 + ( - \frac{12}{5} ) ^{2}}{1 + ( - \frac{12}{5} ) ^{2}}

Simplify

= - \frac{12}{13}

arcsin (\frac{21}{5})

3 sin (6 8^{\circ})

cos (12 2^{\circ})

tan (4 5^{\circ} + 6 0^{\circ})

- 1 sin (0)

What is the value of sin(arctan(-12/5)) ?
The value of sin(arctan(-12/5)) is -12/13