What is the value of sin(2arccos(1/5)) ?

The value of sin(2arccos(1/5)) is (4sqrt(6))/(25)

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sin(2arccos(1/5))

sin (2 arccos (\frac{1}{5}))

\frac{4 6}{25}

Decimal Notation

0.39191 \dots

Solution steps

sin (2 arccos (\frac{1}{5}))

Rewrite using trig identities:

2 sin (arccos (\frac{1}{5})) cos (arccos (\frac{1}{5}))

sin (2 arccos (\frac{1}{5}))

Use the Double Angle identity:

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

= 2 sin (arccos (\frac{1}{5})) cos (arccos (\frac{1}{5}))

= 2 sin (arccos (\frac{1}{5})) cos (arccos (\frac{1}{5}))

Rewrite using trig identities:

sin (arccos (\frac{1}{5})) = \frac{2 6}{5}

sin (arccos (\frac{1}{5}))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{2 6}{5}

Rewrite using trig identities:

cos (arccos (\frac{1}{5})) = \frac{1}{5}

Use the following identity:

cos (arccos (x)) = x

= \frac{1}{5}

= 2 \cdot \frac{2 6}{5} \cdot \frac{1}{5}

Simplify

2 \cdot \frac{2 6}{5} \cdot \frac{1}{5} : \frac{4 6}{25}

2 \cdot \frac{2 6}{5} \cdot \frac{1}{5}

Multiply fractions:

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

= \frac{2 6 \cdot 1 \cdot 2}{5 \cdot 5}

Multiply the numbers:

2 \cdot 1 \cdot 2 = 4

= \frac{4 6}{5 \cdot 5}

Multiply the numbers:

5 \cdot 5 = 25

= \frac{4 6}{25}

= \frac{4 6}{25}

800 sin (4 5^{\circ})

cos (\frac{π}{4} - 2 π)

cos^{2} (3 6^{\circ}) - sin^{2} (3 6^{\circ})

csc (\frac{11 π}{12})

6 tan (3 0^{\circ})

What is the value of sin(2arccos(1/5)) ?
The value of sin(2arccos(1/5)) is (4sqrt(6))/(25)