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

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

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sin(2arccos(-3/5))

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

- \frac{24}{25}

Decimal Notation

- 0.96

Solution steps

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

Rewrite using trig identities:

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

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

Use the Double Angle identity:

sin (2 x) = 2 sin (x) cos (x)

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

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

Rewrite using trig identities:

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

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

Rewrite using trig identities:

sin (arccos (- \frac{3}{5})) = 1 - (- \frac{3}{5})^{2}

Use the following identity:

sin (arccos (x)) = 1 - x^{2}

= 1 - (- \frac{3}{5})^{2}

= 1 - (- \frac{3}{5})^{2}

Simplify

= \frac{4}{5}

Rewrite using trig identities:

cos (arccos (- \frac{3}{5})) = - \frac{3}{5}

Use the following identity:

cos (arccos (x)) = x

= - \frac{3}{5}

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

Simplify

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

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

Remove parentheses:

(- a) = - a

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

Multiply fractions:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

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

Multiply the numbers:

4 \cdot 3 \cdot 2 = 24

= - \frac{24}{5 \cdot 5}

Multiply the numbers:

5 \cdot 5 = 25

= - \frac{24}{25}

= - \frac{24}{25}

- 4 sin (\frac{π}{2})

tan (arccos (- \frac{2}{3}))

sin (arcsin (3))

arctan (\frac{0}{4})

cos (2 \frac{π}{2})

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