Problem

(1 point) A curve with polar equation \[ r=\frac{3}{6 \sin \theta+37 \cos \theta} \] represents a line. Write this line in the given Cartesian form. \[ y= \] ( Note: Your answer should be a function of $x$.)

Solution

Step 1 :Given the polar equation \(r=\frac{3}{6 \sin \theta+37 \cos \theta}\), we want to convert this to Cartesian form.

Step 2 :We know that in polar coordinates, \(x = r\cos(\theta)\) and \(y = r\sin(\theta)\).

Step 3 :Substituting these into the given equation, we get \((x^2 + y^2)^{0.5} - \frac{3}{37\frac{x}{\sqrt{x^2 + y^2}} + 6\frac{y}{\sqrt{x^2 + y^2}}}\).

Step 4 :Solving this equation for \(y\) in terms of \(x\), we find that \(y = 0.5 - 6.16666666666667x\).

Step 5 :Thus, the line in Cartesian form is \(\boxed{y=0.5 - 6.16666666666667x}\).

From Solvely APP
Source: https://solvelyapp.com/problems/20820/

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