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

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

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sin(2arctan(-3/4))

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

- \frac{24}{25}

Solution steps

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

Rewrite using trig identities:

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

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

Rewrite using trig identities:

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

Rewrite using trig identities:

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

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

Simplify

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

= - \frac{24}{25}

arctan (\frac{- 13.79}{25.54})

cos (5 (0))

6 sin (9 0^{\circ})

cos (- 108 0^{\circ})

7 cos (6 5^{\circ})

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