What is the value of sin(2arccos(5/6)) ?

The value of sin(2arccos(5/6)) is (5sqrt(11))/(18)

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sin(2arccos(5/6))

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

\frac{5 11}{18}

Decimal Notation

0.92128 \dots

Solution steps

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

Rewrite using trig identities:

2 sin (arccos (\frac{5}{6})) cos (arccos (\frac{5}{6}))

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

Use the Double Angle identity:

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

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

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

Rewrite using trig identities:

sin (arccos (\frac{5}{6})) = \frac{11}{6}

sin (arccos (\frac{5}{6}))

Rewrite using trig identities:

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

Use the following identity:

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

= 1 - (\frac{5}{6})^{2}

= 1 - (\frac{5}{6})^{2}

Simplify

= \frac{11}{6}

Rewrite using trig identities:

cos (arccos (\frac{5}{6})) = \frac{5}{6}

Use the following identity:

cos (arccos (x)) = x

= \frac{5}{6}

= 2 \cdot \frac{11}{6} \cdot \frac{5}{6}

Simplify

2 \cdot \frac{11}{6} \cdot \frac{5}{6} : \frac{5 11}{18}

2 \cdot \frac{11}{6} \cdot \frac{5}{6}

Multiply fractions:

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

= \frac{11 \cdot 5 \cdot 2}{6 \cdot 6}

Multiply the numbers:

5 \cdot 2 = 10

= \frac{10 11}{6 \cdot 6}

Multiply the numbers:

6 \cdot 6 = 36

= \frac{10 11}{36}

Cancel the common factor:

2

= \frac{5 11}{18}

= \frac{5 11}{18}

\frac{e ^{3} sin ( 3 )}{1 + ( 3 ) ^{2}}

csc (28 5^{\circ})

tan (\frac{2 π}{8})

2 - 2 cosh (2 - 2)

arccos (\frac{17.6}{26})

What is the value of sin(2arccos(5/6)) ?
The value of sin(2arccos(5/6)) is (5sqrt(11))/(18)