By definition, the inverse sine w = arcsin z is the relation such that sin w = z. The inverse cosine w = arccos z is the relation such that cow w = z. The inverse tangent, inverse cotangent, inverse hyperbolic sine, etc., are defined and denoted in a similar fashion. (Note that all these relations are multivalued.) Using sin w = (e^iw- e^-iw)/(2i) and similar representations of cos w, etc., show that

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(a) arccos z = -i In (z + Vz? - 1) |(b) arcsin z = -i In (iz + V1 - z)