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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Find a polar equation for the curve represented by the given cartesian equation x + y = 1
Solution:
Given, the cartesian equation is x + y = 1
Converting to polar coordinates,
x = rcosθ
y = rsinθ
Now, x + y = 1 becomes
rcosθ + rsinθ = 1
r(cosθ + sinθ) = 1
Therefore, the polar equation for the curve is r(cosθ + sinθ) = 1.
Example:
Find a polar equation for the curve represented by the given cartesian equation 3x + y = 5
Solution:
Given, the cartesian equation is x + y = 5
Converting to polar coordinates,
x = rcosθ
y = rsinθ
Now, 3x + y = 5 becomes
3rcosθ + rsinθ = 5
r(3cosθ + sinθ) = 5
Therefore, the polar equation for the curve is r(3cosθ + sinθ) = 5.
Find a polar equation for the curve represented by the given cartesian equation x + y = 1
Summary:
A polar equation for the curve represented by the given cartesian equation x + y = 1 is r(cosθ+sinθ) = 1.
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