What is the value of arcsinh(-8/15) ?

The value of arcsinh(-8/15) is -ln(5/3)

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arcsinh(-8/15)

arcsinh (- \frac{8}{15})

- ln (\frac{5}{3})

Solution steps

arcsinh (- \frac{8}{15})

Use the following property:

arcsinh (- x) = - arcsinh (x)

arcsinh (- \frac{8}{15}) = - arcsinh (\frac{8}{15})

= - arcsinh (\frac{8}{15})

Rewrite using trig identities:

arcsinh (\frac{8}{15}) = ln (\frac{5}{3})

= - ln (\frac{5}{3})

sin (5 0^{\circ}) cos (2 0^{\circ}) - cos (5 0^{\circ}) sin (2 0^{\circ})

sin (6 0^{\circ}) + sin (3 0^{\circ})

cos (2 (2 π))

1 sin (1)

sin (\frac{1}{12} π)