Converting between explicit, implicit and parametric function1. Given an explicit function y = sin ⁡ ( x ) + cos ⁡ ( x ), how to convert it to the respective parametric functions x = f 1 ( t ), y = f 2 ( t )?2. Given parametric functions x = sin ⁡ ( t ) and y = cos ⁡ ( t ), how to obtain the respective implicit function f ( x , y ) = 0?3. Given parametric functions x = 1 + 2 t and y = 3 + 4 t, how to obtain the respective implicit function f ( x , y ) = 0 ?

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Converting between explicit, implicit and parametric function1. Given an explicit function   y  =  sin  ⁡  (  x  )  +  cos  ⁡  (  x  ), how to convert it to the respective parametric functions   x  =      f    1    (  t  ),   y  =      f    2    (  t  )?2. Given parametric functions   x  =  sin  ⁡  (  t  ) and   y  =  cos  ⁡  (  t  ), how to obtain the respective implicit function   f  (  x  ,  y  )  =  0?3. Given parametric functions   x  =  1  +  2  t and   y  =  3  +  4  t, how to obtain the respective implicit function   f  (  x  ,  y  )  =  0 ?

Jaida Sanders · Accepted Answer

Step 11. You can choose for example x as parameter, which leads to:      {                            x          =          t                                      y          =          sin          ⁡          (          t          )          +          cos          ⁡          (          t          )                        Step 22. It is well known that       sin    2    ⁡  (  t  )  +      cos    2    ⁡  (  t  )  =  1 for all   t  ∈      R  . So this curve (I pretend to ignore which curve it is ...) is included in the one with implicit equation:      x    2    +      y    2    =  1and it should be verified that te reverse inclusion is true (provided that t can take any real value, or at least any value in some   [  a  ,  a  +  2  π  ).Step 23. You have to &quot;eliminate&quot; t between those two equations. The first one gives you:   t  =            x      −      1        2  . Putting that in the second one leads to:  y  =  3  +  2  (  x  −  1  )

Converting between explicit, implicit and parametric function 1. Given an explicit function y

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