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

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

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sin(arccos((-2)/3))

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

\frac{5}{3}

Decimal Notation

0.74535 \dots

Solution steps

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

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{5}{3}

sin (10 5^{\circ}) cos (1 5^{\circ})

sin (6 0^{\circ}) \cdot 10

tan (- \frac{π}{9})

arctan (- 3.16)

sin (2 (\frac{π}{12}))

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