What is the inverse mapping of: f ( t ) = ( cos ⁡ ( t ) , sin ⁡ ( t ) )where f : [ 0 , 2 π ) → S 1 Does one just invert the components separately?

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What is the inverse mapping of:  f  (  t  )  =  (  cos  ⁡  (  t  )  ,  sin  ⁡  (  t  )  )where   f  :  [  0  ,  2  π  )  →      S    1  Does one just invert the components separately?

Kamora Greer · Accepted Answer

Step 1Formally, you have       f          −      1        (  cos  ⁡  t  ,  sin  ⁡  t  )  =  t Maybe more practical is the formula      f          −      1        (  x  ,  y  )  =      {                            arccos          ⁡          x                    if                     y          ≥          0                                      2          π          −          arccos          ⁡          x                    if                    y          &amp;lt;          0          ,                        assuming       x    2    +      y    2    =  1 (for instance).

What is the inverse mapping of: f ( t ) = ( cos ⁡ (

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