What is the value of sin(2arcsin(-3/5)) ?

The value of sin(2arcsin(-3/5)) is -24/25

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sin(2arcsin(-3/5))

sin (2 arcsin (- \frac{3}{5}))

- \frac{24}{25}

Solution steps

sin (2 arcsin (- \frac{3}{5}))

Rewrite using trig identities:

- 2 sin (arcsin (\frac{3}{5})) cos (arcsin (\frac{3}{5}))

= - 2 sin (arcsin (\frac{3}{5})) cos (arcsin (\frac{3}{5}))

Rewrite using trig identities:

sin (arcsin (\frac{3}{5})) = \frac{3}{5}

Rewrite using trig identities:

cos (arcsin (\frac{3}{5})) = \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}

1 sin (3 0^{\circ})

40 \cdot cos (3 0^{\circ})

39 (cos (\frac{π}{2}) + i sin (\frac{π}{2}))

cosh (πi)

9 sin (0)

What is the value of sin(2arcsin(-3/5)) ?
The value of sin(2arcsin(-3/5)) is -24/25