102 - Topic 06 - Solving Trigonometric Equations

62 days ago by Professor102

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) = 

Click to the left again to hide and once more to show the dynamic interactive window

show(solns) 
       

                                
                            

                                
arcsin(sqrt(8)/5).n() 
       
0.601264216679128
0.601264216679128