Numerical Methods in Trigonometry•Section 6.2137pointof the function cosx. No matter where you start, you end up getting “drawn” to it.Figure 6.2.2 shows what happens when starting atx=0: taking the cosine of 0 takes you to1, and then successive cosines (indicated by the intersections of the vertical lines with thecosine curve) eventually “spiral” in a rectangular fashion to the fixed point (i.e. the solution),which is the intersection ofy=cosxandy=x.Recall in Example 5.10 in Section 5.2 that we claimed that the maximum and minimum ofthe functiony=cos 6x+sin 4xwere±1.90596111871578, respectively. We can show this byusing the open-source program Octave.2Octave uses asuccessive quadratic programmingmethod to find the minimum of a functionf(x). Finding the maximum off(x) is the same asfinding the minimum of−f(x) then multiplying by−1 (why?). Below we show the commandsto run at the Octave command prompt (octave:n>) to find the minimum off(x)=cos 6x+sin 4x. The commandsqp(3,’f’)
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