What is the value of sin(2arctan(-4/3)) ?

The value of sin(2arctan(-4/3)) is -24/25

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sin(2arctan(-4/3))

sin (2 arctan (- \frac{4}{3}))

- \frac{24}{25}

Solution steps

sin (2 arctan (- \frac{4}{3}))

Rewrite using trig identities:

- 2 sin (arctan (\frac{4}{3})) cos (arctan (\frac{4}{3}))

= - 2 sin (arctan (\frac{4}{3})) cos (arctan (\frac{4}{3}))

Rewrite using trig identities:

sin (arctan (\frac{4}{3})) = \frac{4}{5}

Rewrite using trig identities:

cos (arctan (\frac{4}{3})) = \frac{3}{5}

= - 2 \cdot \frac{4}{5} \cdot \frac{3}{5}

Simplify

- 2 \cdot \frac{4}{5} \cdot \frac{3}{5} : - \frac{24}{25}

= - \frac{24}{25}

arcsin (- \frac{π}{2})

tan (\frac{4 π}{3}) - 3

arctan (\frac{9.3}{7.5})

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

sin (arcsec (4))

What is the value of sin(2arctan(-4/3)) ?
The value of sin(2arctan(-4/3)) is -24/25