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

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

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sin(2arcsin(4/5))

sin (2 arcsin (\frac{4}{5}))

\frac{24}{25}

Decimal Notation

0.96

Solution steps

sin (2 arcsin (\frac{4}{5}))

Rewrite using trig identities:

2 sin (arcsin (\frac{4}{5})) cos (arcsin (\frac{4}{5}))

sin (2 arcsin (\frac{4}{5}))

Use the Double Angle identity:

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

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

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

Rewrite using trig identities:

sin (arcsin (\frac{4}{5})) = \frac{4}{5}

Use the following identity:

sin (arcsin (x)) = x

= \frac{4}{5}

Rewrite using trig identities:

cos (arcsin (\frac{4}{5})) = \frac{3}{5}

cos (arcsin (\frac{4}{5}))

Rewrite using trig identities:

cos (arcsin (\frac{4}{5})) = 1 - (\frac{4}{5})^{2}

Use the following identity:

cos (arcsin (x)) = 1 - x^{2}

= 1 - (\frac{4}{5})^{2}

= 1 - (\frac{4}{5})^{2}

Simplify

= \frac{3}{5}

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

Simplify

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

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

Convert element to fraction:

2 = \frac{2}{1}

= \frac{2}{1} \cdot \frac{4}{5} \cdot \frac{3}{5}

Multiply fractions:

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

= \frac{2 \cdot 4 \cdot 3}{1 \cdot 5 \cdot 5}

Multiply the numbers:

2 \cdot 4 \cdot 3 = 24

= \frac{24}{1 \cdot 5 \cdot 5}

Multiply the numbers:

1 \cdot 5 \cdot 5 = 25

= \frac{24}{25}

= \frac{24}{25}

arcsin (- 0.75)

sin (4 5^{\circ}) \cdot 10

cos (- \frac{3}{4} π)

sin^{2} (\frac{1}{4})

cos (\frac{3 π}{2}) + i sin (\frac{3 π}{2})

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