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} \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}

3 cos (\frac{π}{6})

tan (\frac{17 π}{4})

cos (\frac{1}{5})

arcsin (1.33)

cos (6 9^{\circ})

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