Problems 1-10 : Convert each polar equation to rectangular form.
Problem 1 :
r = 2
Problem 2 :
tan θ = 2
Problem 3 :
Problem 4 :
r sin θ = 3
Problem 5 :
r = 2cos θ
Problem 6 :
r = 4cos θ - 4sin θ
Problem 7 :
r = 2cos θ + 2sin θ
Problem 8 :
Problem 9 :
Problem 10 :
r2 = 5 sec (2θ)
Problems 11-16 : Convert each rectangular equation to polar form.
Problem 11 :
x = y2
Problem 12 :
y = x2
Problem 13 :
2x - 5y = 4
Problem 14 :
x2 + y2 = 9
Problem 15 :
x2 + y2 - 7y = 0
Problem 16 :
(x - 1)2 + (y + 1)2 = 2
1. Answer :
r = 2
Squaring both sides,
r2 = 4
Substitute x2 + y2 for r2.
x2 + y2 = 4
2. Answer :
tan θ = 2
Multiply both sides by x.
y = 2x
3. Answer :
Take tan on both sides.
4. Answer :
r sin θ = 3
Substitute y for r sin θ.
y = 3
5. Answer :
r = 2cos θ
Multiply both sides by r.
r2 = 2rcos θ
Substitute x2 + y2 for r2 and x for r cos θ.
x2 + y2 = 2x
x2 + y2 = 2x
x2 - 2x + y2 = 0
x2 - 2(x)(1) + y2 = 0
x2 - 2(x)(1) + 12 - 12 + y2 = 0
(x - 1)2 - 12 + y2 = 0
(x - 1)2 - 1 + y2 = 0