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.
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 = 4
Solution:
Given, the cartesian equation is x + y = 4
Converting to polar coordinates,
x = r cosθ
y = r sinθ
Now, x + y = 4 becomes
r cosθ + r sinθ = 4
r (cosθ + sinθ) = 4
Therefore, the polar equation for the curve is r(cosθ + sinθ) = 4.
Example:
Find a polar equation for the curve represented by the given cartesian equation 3x + 4y = 5
Solution:
Given, the cartesian equation is 3x + 4y = 5
Converting to polar coordinates,
x = rcosθ
y = rsinθ
Now, 3x + 4y = 5 becomes
3rcosθ + 4rsinθ = 5
r(3cosθ + 4sinθ) = 5
Therefore, the polar equation for the curve is r(3cosθ + 4sinθ) = 5.
Find a polar equation for the curve represented by the given cartesian equation. x + y = 4
Summary:
A polar equation for the curve represented by the given cartesian equation x + y = 4 is r(cosθ + sinθ) = 4.
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