Respuesta :

Answer:

(1, -1)

Step-by-step explanation:

To convert polar to rectangular coordinates, use these identities:

  • x = rcos(Ф)
  • y = rsin(Ф)
  • x² + y² = r²  

Here we were given the point [tex](\sqrt{2},-\frac{\pi}{4})[/tex] which is our (r, Ф) point

We can now plug these values into our x and y equations to convert to rectangular and find our (x, y) point

  • x = [tex](\sqrt{2} )cos(-\frac{\pi}{4} )= (\sqrt{2})(\frac{\sqrt{2} }{2})=\frac{2}{2}=1[/tex]
  • y = [tex](\sqrt{2} )sin(-\frac{\pi}{4} )= (\sqrt{2})(-\frac{\sqrt{2} }{2})=-\frac{2}{2}=-1[/tex]

So our (x, y) point is (1, -1)

  • [tex](\sqrt{2},-\frac{\pi}{4}) = (1, -1)[/tex]
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