What is the value of sin(2arcsin(-1/3)) ?

The value of sin(2arcsin(-1/3)) is -(4sqrt(2))/9

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sin(2arcsin(-1/3))

sin (2 arcsin (- \frac{1}{3}))

- \frac{4 2}{9}

Solution steps

sin (2 arcsin (- \frac{1}{3}))

Rewrite using trig identities:

- 2 sin (arcsin (\frac{1}{3})) cos (arcsin (\frac{1}{3}))

= - 2 sin (arcsin (\frac{1}{3})) cos (arcsin (\frac{1}{3}))

Rewrite using trig identities:

sin (arcsin (\frac{1}{3})) = \frac{1}{3}

Rewrite using trig identities:

cos (arcsin (\frac{1}{3})) = \frac{2 2}{3}

= - 2 \cdot \frac{1}{3} \cdot \frac{2 2}{3}

Simplify

- 2 \cdot \frac{1}{3} \cdot \frac{2 2}{3} : - \frac{4 2}{9}

= - \frac{4 2}{9}

sin (\frac{π}{3}) - cos (\frac{π}{3})

cos^{2} (1) - e^{- 2}

arctan (\frac{- 5}{- 2})

arctan (0.77)

- 1 (sin (0))

What is the value of sin(2arcsin(-1/3)) ?
The value of sin(2arcsin(-1/3)) is -(4sqrt(2))/9