What is the value of arccosh(0) ?

The value of arccosh(0) is ln(i)

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arccosh(0)

arccosh (0)

ln (i)

Solution steps

arccosh (0)

Use the Hyperbolic identity:

arccosh (x) = ln (x + x^{2} - 1)

= ln (0 + 0^{2} - 1)

Simplify

ln (0 + 0^{2} - 1) : ln (i)

ln (0 + 0^{2} - 1)

Apply rule

0^{a} = 0

0^{2} = 0

= ln (0 + 0 - 1)

0 - 1 = i

0 - 1

Subtract the numbers:

0 - 1 = - 1

= - 1

Apply imaginary number rule:

- 1 = i

= i

= ln (0 + i)

0 + i = i

= ln (i)

= ln (i)

arctan (\frac{- 3}{- 1})

cosh (- 1)

8 cos (4 5^{\circ})

- 2 sin (\frac{π}{6})

csc (- 21 0^{\circ})