Question

Convert the polar coordinates to rectangular form (√2,-π\4)

Answer 1

(1, -1)

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
`(√(2),-(\pi)/(4))` 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 =
  `(√(2) )cos(-(\pi)/(4) )= (√(2))((√(2) )/(2))=(2)/(2)=1`
• y =
  `(√(2) )sin(-(\pi)/(4) )= (√(2))(-(√(2) )/(2))=-(2)/(2)=-1`

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

• 
  `(√(2),-(\pi)/(4)) = (1, -1)`