Textbook Question
In Exercises 54–60, convert each polar equation to a rectangular equation. Then use your knowledge of the rectangular equation to graph the polar equation in a polar coordinate system. θ = 3π/4
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9. Polar Equations
Convert Equations Between Polar and Rectangular Forms
Multiple Choice
Convert each equation to its polar form.
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Verified step by step guidance1
Identify the given Cartesian equation: y - x = 6.
Recall the conversion formulas from Cartesian to polar coordinates: x = r \(\cos\[\theta\) and y = r \(\sin\]\theta\).
Substitute the polar coordinate expressions into the Cartesian equation: r \(\sin\[\theta\) - r \(\cos\]\theta\) = 6.
Factor out r from the left side of the equation: r(\(\sin\[\theta\) - \(\cos\]\theta\)) = 6.
Solve for r by dividing both sides by (\(\sin\[\theta\) - \(\cos\]\theta\)): r = \(\frac{6}{\sin\theta - \cos\theta}\).
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