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A passenger on a stopped bus notices that rain is falling vertically just outside the window. When the bus moves with constant velocity, the passenger observes that the falling raindrops are now making an angle of with respect to the vertical. What is the ratio of the speed of the raindrops to the speed of the bus ?
The Maclaurin series expansion for cos x is
Starting with the simplest version, , add terms one at a time to estimate
After each new term is added, compute the true and approximate percent relative errors. Use your pocket calculator to determine the true value. Add terms until the absolute value of the approximate error estimate falls below an error criterion conforming to two significant figures.
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