113 - Topic 06 - Solving Trigonometric Equations -- Sage

Finding the family of solutions for equations involving Trigonometric functions

John Travis

Mississippi College

%hide %auto reset() var('x,y') @interact def _(f = input_box((sin(2*x)-2*sin(x))*(cos(x) - 1/2),label='0 = f(x) =')): global solns solns = f._maxima_().to_poly_solve(x).sage() #solns = solve(f.expand_trig().factor(),x,solution_dict=true) G = plot(f,x,-1,7) show(G) #g(z8,z10,z12,z14) = solns[0][0] #H=implicit_plot(g(z10=0),(x,-1,7),(y,-3,3)) #show(solns+H) n = len(solns) for k in range(n): html('Solution to equation: $%s$'%str(latex(solns[k][0])))

0 = f(x) =

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arcsin(3/4).n()

0.848062078981481

0.848062078981481

show(solns)

$\newcommand{\Bold}[1]{\mathbf{#1}}\left[\left[x = 2 \, \pi z_{83} + \arctan\left(-\frac{\sqrt{4 \, \sqrt{2} - 2}}{\sqrt{2} - 2}\right) - i \, \log\left(\frac{1}{2} \, \sqrt{{\left(\sqrt{2} - 2\right)}^{2} + 4 \, \sqrt{2} - 2}\right)\right], \left[x = 2 \, \pi z_{85} + \arctan\left(\frac{\sqrt{4 \, \sqrt{2} - 2}}{\sqrt{2} - 2}\right) - i \, \log\left(\frac{1}{2} \, \sqrt{{\left(\sqrt{2} - 2\right)}^{2} + 4 \, \sqrt{2} - 2}\right)\right], \left[x = 2 \, \pi z_{87} - i \, \log\left(\frac{1}{2} \, \sqrt{2} - \frac{1}{2} \, \sqrt{4 \, \sqrt{2} + 2} + 1\right)\right], \left[x = 2 \, \pi z_{89} - i \, \log\left(\frac{1}{2} \, \sqrt{2} + \frac{1}{2} \, \sqrt{4 \, \sqrt{2} + 2} + 1\right)\right]\right]$

(1/2)*arctan(sqrt(34)*4/9).n()

0.601264216679128

0.601264216679128

arcsin(sqrt(8)/5).n()

0.601264216679128

0.601264216679128

113 - Topic 06 - Solving Trigonometric Equations

319 days ago by Professor113

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