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Pre-Calc Exam Notes 137

Pre-Calc Exam Notes 137 - Numerical Methods in Trigonometry...

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Numerical Methods in Trigonometry Section 6.2 137 point of the function cos x . No matter where you start, you end up getting “drawn” to it. Figure 6.2.2 shows what happens when starting at x = 0: taking the cosine of 0 takes you to 1, and then successive cosines (indicated by the intersections of the vertical lines with the cosine curve) eventually “spiral” in a rectangular fashion to the fixed point (i.e. the solution), which is the intersection of y = cos x and y = x . Recall in Example 5.10 in Section 5.2 that we claimed that the maximum and minimum of the function y = cos 6 x + sin 4 x were ± 1 . 90596111871578, respectively. We can show this by using the open-source program Octave. 2 Octave uses a successive quadratic programming method to find the minimum of a function f ( x ). Finding the maximum of f ( x ) is the same as finding the minimum of f ( x ) then multiplying by 1 (why?). Below we show the commands to run at the Octave command prompt ( octave:n> ) to find the minimum of f ( x ) = cos 6 x + sin 4 x . The command sqp(3,’f’)
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