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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show(solns)

$\newcommand{\Bold}[1]{\mathbf{#1}}\left[\left[x = \pi + 2 \, \pi z_{41}\right], \left[x = 2 \, \pi z_{43}\right], \left[x = -\frac{1}{3} \, \pi + 2 \, \pi z_{45}\right], \left[x = \frac{1}{3} \, \pi + 2 \, \pi z_{47}\right]\right]$

(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

351 days ago by Professor102

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