What is the value of sin(2arcsin(0)) ?

The value of sin(2arcsin(0)) is 0

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sin(2arcsin(0))

sin (2 arcsin (0))

0

Solution steps

sin (2 arcsin (0))

Rewrite using trig identities:

2 sin (arcsin (0)) cos (arcsin (0))

sin (2 arcsin (0))

Use the Double Angle identity:

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

= 2 sin (arcsin (0)) cos (arcsin (0))

= 2 sin (arcsin (0)) cos (arcsin (0))

Rewrite using trig identities:

sin (arcsin (0)) = 0

Use the following identity:

sin (arcsin (x)) = x

= 0

Rewrite using trig identities:

cos (arcsin (0)) = 1

cos (arcsin (0))

Rewrite using trig identities:

cos (arcsin (0)) = 1 - 0^{2}

Use the following identity:

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

= 1 - 0^{2}

= 1 - 0^{2}

Simplify

= 1

= 2 \cdot 0 \cdot 1

Simplify

= 0

arctan (\frac{0}{- 6})

cos (2 0^{\circ}) cos (1 0^{\circ}) - sin (2 0^{\circ}) sin (1 0^{\circ})

cos (2 5^{\circ}) cos (1 5^{\circ}) - sin (2 5^{\circ}) sin (1 5^{\circ})

1 + sec^{2} (π)

arcsin (\frac{4}{11})