Is sin-1(2i) Equal to 0.5 + 1.31696i?

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Discussion Overview

The discussion centers around the evaluation of the expression sin-1(2i) and its potential equality to 0.5 + 1.31696i. Participants explore the mathematical implications of this expression, including its multi-valued nature and the methods for solving it.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant questions the value of sin-1(2i) and seeks clarification on its evaluation.
  • Another participant presents a formula for sin(x) and suggests substituting y = exp(ix) to solve for x.
  • A third participant notes that solving the equation (y + 1/y)/2i = 2i will yield two values for y, indicating the multi-valued nature of the solution.
  • There is a challenge regarding the formulation of the equation, with one participant suggesting it should be (y - 1/y)/2i = 2i instead.
  • One participant expresses confusion over their own suggestion, indicating uncertainty in the discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct formulation of the equation or the evaluation of sin-1(2i). Multiple competing views and uncertainties remain regarding the approach to solving the problem.

Contextual Notes

The discussion highlights the complexity of evaluating sin-1(2i), including the implications of multi-valued solutions and the potential for different interpretations of the equations involved.

symsane
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I could not found any answer to this question: What is sin-1(2i) equal?
 
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sin(x) = (exp(ix)-exp(-ix))/2i

Firstly let y=exp(ix) and subs in

( y + 1/y)/2i=2i

solve for y, then for x.
 


Since you titled this thread "Multi-Valuedness", note that solving (y+ 1/y)/2i= 2i will involve solving a quadratic function so you may have two values for y. Then solving y= exp(ix) with both values of involves taking the logarithm which adds multiples of 2\pi i.
 


For the two last posts, isn't it supposed to be (y - 1/y)/2i = 2i ?
 


Yes - I can't even seem to follow my own suggestion.
 

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