A curve in polar form r = f () has parametrization r() = f ()cos ,sin Let be the angle

Chapter 13, Problem 64

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A curve in polar form r = f () has parametrization r() = f ()cos ,sin Let be the angle between the radial and tangent vectors (Figure 10). Prove that tan = r dr/d = f () f () Hint: Compute r() r () and r() r (). r'( ) r( ) y x FIGURE 10 Curve with polar parametrization r() = f ()cos ,sin . 65.

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