What is the value of arctanh(-1) ?

The value of arctanh(-1) is Undefined

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arctanh(-1)

arctanh (- 1)

Undefined

Solution steps

arctanh (- 1)

Use the following property:

arctanh (- x) = - arctanh (x)

arctanh (- 1) = - arctanh (1)

= - arctanh (1)

Rewrite using trig identities:

arctanh (1) =

Undefined

arctanh (1)

Use the Hyperbolic identity:

arctanh (x) = \frac{ln ( \frac{1 + x}{1 - x} )}{2}

= \frac{ln ( \frac{1 + 1}{1 - 1} )}{2}

Simplify

\frac{ln ( \frac{1 + 1}{1 - 1} )}{2} :

Undefined

\frac{ln ( \frac{1 + 1}{1 - 1} )}{2}

1 - 1 = 0

= \frac{ln ( \frac{1 + 1}{0} )}{2}

\frac{x}{0}

is undefined

= Undefined

= Undefined

= Undefined

3 cos (- 3)

\frac{1 + sin ( 4 0 ^{\circ} )}{sin ( 6 5 ^{\circ} )}

arcsin (- \frac{8}{17})

cos (\frac{π}{3}) + i \cdot sin (\frac{π}{3})

\frac{10 sin ( 5 0 ^{\circ} )}{sin ( 7 5 ^{\circ} )}