What is the value of sin(2arccos(-4/5)) ?

The value of sin(2arccos(-4/5)) is -24/25

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sin(2arccos(-4/5))

sin (2 arccos (- \frac{4}{5}))

- \frac{24}{25}

Solution steps

sin (2 arccos (- \frac{4}{5}))

Rewrite using trig identities:

2 sin (arccos (- \frac{4}{5})) cos (arccos (- \frac{4}{5}))

= 2 sin (arccos (- \frac{4}{5})) cos (arccos (- \frac{4}{5}))

Rewrite using trig identities:

sin (arccos (- \frac{4}{5})) = \frac{3}{5}

Rewrite using trig identities:

cos (arccos (- \frac{4}{5})) = - \frac{4}{5}

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

Simplify

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

= - \frac{24}{25}

tan (2 arcsin (- \frac{4}{5}))

cos (84 0^{\circ})

tan (- \frac{4}{3})

sin^{2} (27 0^{\circ})

cot (- 2)

What is the value of sin(2arccos(-4/5)) ?
The value of sin(2arccos(-4/5)) is -24/25