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How to find a Cartesian equation for a polar curve?
How do I find a Cartesian equation for the polar curves:
A) r = 2cscΘ
B) r = 2tanΘsecΘ
If someone could show step by step how to solve this problem it would be helpful.
2 Answers
- 10 years agoFavorite Answer
x = rcosΘ
y = rsinΘ
tanΘ = y/x
r = √(x² + y²)
A) r = 2cscΘ
r = 2/sinΘ
2 = rsinΘ
y = 2
B) r = 2tanΘsecΘ
r = 2tanΘ/cosΘ
rcosΘ = 2tanΘ
x = 2(y/x)
x² = 2y
y = 1/2 x²
- ?Lv 710 years ago
A) y = r*sin(t)
y = 2csc(t)*sin(t) = 2
y = [2/sin(t)]*sin(t)
y = 2
B) r = 2tan(t)*1/cos(t)
x = 2tan(t)*1/cos(t)*cos(t) = 2tan(t)
tan(t) = x/2
y = 2tan(t)*1/cos(t)*sin(t) = 2tan^2(t)
y = 2*x^/4 = x^2/2
y = (1/2)*x^2
