What is the value of sin(2arcsin(-1/3)) ?

The value of sin(2arcsin(-1/3)) is -(4sqrt(2))/9

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(2arcsin(-1/3))

sin (2 arcsin (- \frac{1}{3}))

- \frac{4 2}{9}

Decimal Notation

- 0.62853 \dots

Solution steps

sin (2 arcsin (- \frac{1}{3}))

Rewrite using trig identities:

- 2 sin (arcsin (\frac{1}{3})) cos (arcsin (\frac{1}{3}))

sin (2 arcsin (- \frac{1}{3}))

Use the Double Angle identity:

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

= 2 sin (arcsin (- \frac{1}{3})) cos (arcsin (- \frac{1}{3}))

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{1}{3}) = - arcsin (\frac{1}{3})

= 2 sin (arcsin (- \frac{1}{3})) cos (- arcsin (\frac{1}{3}))

Use the following property:

cos (- x) = cos (x)

cos (- arcsin (\frac{1}{3})) = cos (arcsin (\frac{1}{3}))

= 2 sin (arcsin (- \frac{1}{3})) cos (arcsin (\frac{1}{3}))

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{1}{3}) = - arcsin (\frac{1}{3})

= 2 sin (- arcsin (\frac{1}{3})) cos (arcsin (\frac{1}{3}))

Use the following property:

sin (- x) = - sin (x)

sin (- arcsin (\frac{1}{3})) = - sin (arcsin (\frac{1}{3}))

= 2 (- sin (arcsin (\frac{1}{3}))) cos (arcsin (\frac{1}{3}))

Simplify

= - 2 sin (arcsin (\frac{1}{3})) cos (arcsin (\frac{1}{3}))

= - 2 sin (arcsin (\frac{1}{3})) cos (arcsin (\frac{1}{3}))

Rewrite using trig identities:

sin (arcsin (\frac{1}{3})) = \frac{1}{3}

Use the following identity:

sin (arcsin (x)) = x

= \frac{1}{3}

Rewrite using trig identities:

cos (arcsin (\frac{1}{3})) = \frac{2 2}{3}

cos (arcsin (\frac{1}{3}))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{2 2}{3}

= - 2 \cdot \frac{1}{3} \cdot \frac{2 2}{3}

Simplify

- 2 \cdot \frac{1}{3} \cdot \frac{2 2}{3} : - \frac{4 2}{9}

- 2 \cdot \frac{1}{3} \cdot \frac{2 2}{3}

Multiply fractions:

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

= - \frac{1 \cdot 2 2 \cdot 2}{3 \cdot 3}

Multiply the numbers:

1 \cdot 2 \cdot 2 = 4

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

Multiply the numbers:

3 \cdot 3 = 9

= - \frac{4 2}{9}

= - \frac{4 2}{9}

sin (\frac{π}{3}) - cos (\frac{π}{3})

cos^{2} (1) - e^{- 2}

arctan (\frac{- 5}{- 2})

arctan (0.77)

- 1 (sin (0))

What is the value of sin(2arcsin(-1/3)) ?
The value of sin(2arcsin(-1/3)) is -(4sqrt(2))/9