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

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

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sin(2arcsin(-1/2))

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

- \frac{3}{2}

Solution steps

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

Rewrite using trig identities:

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

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

Rewrite using trig identities:

sin (arcsin (\frac{1}{2})) = \frac{1}{2}

Rewrite using trig identities:

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

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

Simplify

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

= - \frac{3}{2}

[3 (cos (\frac{π}{12}) + sin (\frac{π}{12}))]^{3}

π - sin (π)

arctan (- 0.75)

3 cos (2)

ln (sec (0))

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