The letters r and è represent polar coordinates. Write the equation using rectangular coordinates (x,y).
r=1+2sinè
I know that I have to use something along the lines of x=rcosè and y=rsinè, but I'm stuck when I try to figure it out. Can someone help? Thank you!
r = √(x^2 + y^2) and sinØ = y/r , so
r = 1 + 2y/r
multiply both sides by r
r^2 = r + 2y
x^2 + y^2 = √(x^2 + y^2) + 2y
Thanks! That makes sense. One step closer to passing my final exam tomorrow!
Certainly! To convert the equation from polar coordinates to rectangular coordinates, you can use the following formulas:
x = r * cos(è)
y = r * sin(è)
Given that r = 1 + 2sin(è), we can substitute these equations into the formulas above to get the equation in rectangular coordinates.
Substituting r = 1 + 2sin(è) into x = r * cos(è):
x = (1 + 2sin(è)) * cos(è)
Substituting r = 1 + 2sin(è) into y = r * sin(è):
y = (1 + 2sin(è)) * sin(è)
Therefore, the equation in rectangular coordinates (x, y) is:
x = (1 + 2sin(è)) * cos(è)
y = (1 + 2sin(è)) * sin(è)
I hope that helps! Let me know if you have any further questions.