By Definition The Inverse Sine W Arc Sin Z

By definition, the inverse sine w = arc sinzis the relation such that sin w = z. The inverse cosine w – arcos z is the relation such that cos w = z. The inverse tangent, increase cotangent, inverse hyperbolic sine, etc, are defined and denoted in a similar fashion. (Note that all these relations are multi valued.) Using sin w = (eiw– e–iw)/(2i) and similar representations of cos, w etc. show that 

By definition, the inverse sine w = arc sin z

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