janhardo

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These are answers submitted by janhardo

..as you can see here :
 Each trigonometric function in terms of each of the other five List of trigonometric identities - Wikipedia

(all this mathematical knowledge here on wiki is included in Maple i think) 

Knowing the unit circle and all the graphs of sin, cos , tan for deducing some formulas and for goniometric equations.

Manual adding table in Maple and then add plots into the cells is probably not useful for you?

Got this from someone else here on forum

restart

NULL

NULLz := x+I*y

````

Plts := seq(plot3d([Re(k*log(z)), Im(k*log(z))], x = -3 .. 3, y = -3 .. 3, labels = ["Re(z)", "Im(z)", " ln(z)"], size = [800, 800]), k = [1, 2, 4, 6])
NULL

NULL

 

Plts[1]

Plts[2]

Plts[3]

Plts[4]

 

 

plots:-display(Plts)

NULL

Download complex_log_plot.mw




f := x -> x^sin(x):

Inflpts := [fsolve(D(D(f))(x), x=0..16, maxsols=6)];

Q := map(p->[p,f(p)], Inflpts):

T := seq(plot(D(f)(p)*(x-p)+f(p), x=p-1..p+1, color=red), p=Inflpts):

plots:-display(plot(f, 0.0..16.0, color=black), T,

        plots:-pointplot(Q, symbolsize=10, symbol=solidcircle, color=blue),

        map(p->plots:-textplot(evalf[4]([p[1]-sign(D(f)(p[1]))*2/3,p[2]+1,p]),

                               font=[Times,8]),Q), size=[800,400]);

a example fo infliction points, can be adjusted for find min/max  :to give a idea

with(Student[Basics]);
  [ExpandSteps, FactorSteps, LinearSolveSteps, LongDivision, 

    OutputStepsRecord, PracticeSheet, SolveSteps]


-----------------------------------------------------------------

FactorSteps(Y^2*x^3-x^3);  
How about for complex numbers ?

Given a polynome in C : z^4-2.z^3+ 3.z^2-2.z+2

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