Convert the polar equation r-3cosx = 5sinx in Cartesian equation form.
To convert the given polar equation into Cartesian equation form, we will use the following trigonometric identities:
r = sqrt(x^2 + y^2)
sin(x) = y / r
cos(x) = x / r
Let's start by rearranging the given polar equation:
r - 3cos(x) = 5sin(x)
Substitute the values of sin(x) and cos(x) using the above trigonometric identities:
sqrt(x^2 + y^2) - 3(x / sqrt(x^2 + y^2)) = 5(y / sqrt(x^2 + y^2))
Next, we can simplify the equation by multiplying both sides by sqrt(x^2 + y^2) to eliminate the square roots:
x^2 + y^2 - 3x = 5y
Finally, rearrange the equation to obtain the Cartesian equation form:
x^2 - 3x + y^2 - 5y = 0
Therefore, the Cartesian equation form of the given polar equation r - 3cos(x) = 5sin(x) is x^2 - 3x + y^2 - 5y = 0.
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