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

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

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sin(2arcsin(-(sqrt(2))/2))

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

- 1

Solution steps

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

Rewrite using trig identities:

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

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

Use the Double Angle identity:

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

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

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{2}{2}) = - arcsin (\frac{2}{2})

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

Use the following property:

cos (- x) = cos (x)

cos (- arcsin (\frac{2}{2})) = cos (arcsin (\frac{2}{2}))

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

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{2}{2}) = - arcsin (\frac{2}{2})

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

Use the following property:

sin (- x) = - sin (x)

sin (- arcsin (\frac{2}{2})) = - sin (arcsin (\frac{2}{2}))

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

Simplify

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

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

Rewrite using trig identities:

sin (arcsin (\frac{2}{2})) = \frac{2}{2}

Use the following identity:

sin (arcsin (x)) = x

= \frac{2}{2}

Rewrite using trig identities:

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

cos (arcsin (\frac{2}{2}))

Rewrite using trig identities:

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

Use the following identity:

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

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

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

Simplify

= \frac{1}{2}

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

Simplify

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

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

Multiply fractions:

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

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

Cancel the common factor:

2

= - 2 \frac{1}{2}

Apply radical rule:

a b = a \cdot b

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

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

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

2 \cdot \frac{1}{2}

Multiply fractions:

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

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

Cancel the common factor:

2

= 1

= - 1

Apply rule

1 = 1

= - 1

= - 1

2 cos (0) + sin (0)

\frac{tan ( - \frac{2 π}{3} )}{sin ( \frac{7 π}{4} )} - sec (- π)

tan (- \frac{5 π}{8})

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arcsin (0.82)

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