What is the value of sin(2arcsin(-5/13)) ?

The value of sin(2arcsin(-5/13)) is -120/169

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sin(2arcsin(-5/13))

sin (2 arcsin (- \frac{5}{13}))

- \frac{120}{169}

Decimal Notation

- 0.71005 \dots

Solution steps

sin (2 arcsin (- \frac{5}{13}))

Rewrite using trig identities:

- 2 sin (arcsin (\frac{5}{13})) cos (arcsin (\frac{5}{13}))

sin (2 arcsin (- \frac{5}{13}))

Use the Double Angle identity:

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

= 2 sin (arcsin (- \frac{5}{13})) cos (arcsin (- \frac{5}{13}))

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{5}{13}) = - arcsin (\frac{5}{13})

= 2 sin (arcsin (- \frac{5}{13})) cos (- arcsin (\frac{5}{13}))

Use the following property:

cos (- x) = cos (x)

cos (- arcsin (\frac{5}{13})) = cos (arcsin (\frac{5}{13}))

= 2 sin (arcsin (- \frac{5}{13})) cos (arcsin (\frac{5}{13}))

Use the following property:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{5}{13}) = - arcsin (\frac{5}{13})

= 2 sin (- arcsin (\frac{5}{13})) cos (arcsin (\frac{5}{13}))

Use the following property:

sin (- x) = - sin (x)

sin (- arcsin (\frac{5}{13})) = - sin (arcsin (\frac{5}{13}))

= 2 (- sin (arcsin (\frac{5}{13}))) cos (arcsin (\frac{5}{13}))

Simplify

= - 2 sin (arcsin (\frac{5}{13})) cos (arcsin (\frac{5}{13}))

= - 2 sin (arcsin (\frac{5}{13})) cos (arcsin (\frac{5}{13}))

Rewrite using trig identities:

sin (arcsin (\frac{5}{13})) = \frac{5}{13}

Use the following identity:

sin (arcsin (x)) = x

= \frac{5}{13}

Rewrite using trig identities:

cos (arcsin (\frac{5}{13})) = \frac{12}{13}

cos (arcsin (\frac{5}{13}))

Rewrite using trig identities:

cos (arcsin (\frac{5}{13})) = 1 - (\frac{5}{13})^{2}

Use the following identity:

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

= 1 - (\frac{5}{13})^{2}

= 1 - (\frac{5}{13})^{2}

Simplify

= \frac{12}{13}

= - 2 \cdot \frac{5}{13} \cdot \frac{12}{13}

Simplify

- 2 \cdot \frac{5}{13} \cdot \frac{12}{13} : - \frac{120}{169}

- 2 \cdot \frac{5}{13} \cdot \frac{12}{13}

Convert element to fraction:

2 = \frac{2}{1}

= \frac{2}{1} \cdot \frac{5}{13} \cdot \frac{12}{13}

Multiply fractions:

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

= - \frac{2 \cdot 5 \cdot 12}{1 \cdot 13 \cdot 13}

Multiply the numbers:

2 \cdot 5 \cdot 12 = 120

= - \frac{120}{1 \cdot 13 \cdot 13}

Multiply the numbers:

1 \cdot 13 \cdot 13 = 169

= - \frac{120}{169}

= - \frac{120}{169}

cot (6 5^{\circ})

cos^{2} (3 7^{\circ})

cos (\frac{5 π}{12}) - cos (\frac{π}{12})

csc (\frac{5 π}{12})

tan (4 5^{\circ} + 3 0^{\circ})

What is the value of sin(2arcsin(-5/13)) ?
The value of sin(2arcsin(-5/13)) is -120/169