Multiple Choice
Given the point in cylindrical coordinates , what are its spherical coordinates ?
9. Polar Equations
Convert Points Between Polar and Rectangular Coordinates
Multiple Choice
Convert the point to rectangular coordinates.
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Verified step by step guidance1
Identify the given polar coordinates: (r, θ) = (-2, -\(\frac{\pi}{4}\)).
Recall the formulas to convert polar coordinates to rectangular coordinates: x = r \(\cdot\) \(\cos\)(θ) and y = r \(\cdot\) \(\sin\)(θ).
Substitute the given values into the formulas: x = -2 \(\cdot\) \(\cos\)(-\(\frac{\pi}{4}\)) and y = -2 \(\cdot\) \(\sin\)(-\(\frac{\pi}{4}\)).
Calculate \(\cos\)(-\(\frac{\pi}{4}\)) and \(\sin\)(-\(\frac{\pi}{4}\)). Remember that \(\cos\)(-θ) = \(\cos\)(θ) and \(\sin\)(-θ) = -\(\sin\)(θ).
Simplify the expressions to find the rectangular coordinates (x, y).
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