Questions: Sketch the curve with the given polar equation by first sketching the graph of r as a function of θ in Cartesian coordinates. r^2 = 4 sin(2θ)

Transcript text: Sketch the curve with the given polar equation by first sketching the graph of $r$ as a function of $\theta$ in Cartesian coordinates. \[ r^{2}=4 \sin (2 \theta) \]

Solution

Solution Steps

Step 1: Rewrite the polar equation

Given the polar equation: \[ r^{2}=4 \sin (2 \theta) \]

Step 2: Solve for $ r $

To solve for $ r $, we take the square root of both sides: \[ r = \sqrt{4 \sin (2 \theta)} \] \[ r = 2 \sqrt{\sin (2 \theta)} \]

Final Answer

The polar equation in terms of $ r $ and $ \theta $ is: \[ r = 2 \sqrt{\sin (2 \theta)} \]

{"axisType": 2, "coordSystem": {"xmin": -3, "xmax": 3, "ymin": -2, "ymax": 2}, "commands": ["r = 2sqrt(sin(2\u03b8))"], "latex_expressions": ["$r = 2 \\sqrt{\\sin (2 \theta)}$"]}

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