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Hello Everyone

 

I have an expression which I would like to integrate from x=0 to x=L. The expression is 

x1:=(sin(beta*x)*cos(m*Pi*x/L))/(1+alpha*x)

 

Here, beta, m, alpha are constant. However I want the result in terms of these quantities.

 

I will be grateful if you could help mw in this regard.

Thanks a lot.

Hello,

I would like to solve this equation :

tan(gamma0(t)) = tan(gamma[1](t)-theta[1](t)-psi[1](t)

I would like to select the solution of arctan by assuming the domain of variation of some variables. In my case, if -Pi/2 < gamma[1](t) - theta[1](t) - psi[1](t) < Pi/2, the arctan gives only one solution.

Can you help me to solve this equation ? 

eq:=tan(gamma0(t)) = tan(gamma[1](t)-theta[1](t)-psi[1](t))
solve(eq,gamma0(t)) assuming -Pi/2 < gamma[1](t) - theta[1](t) - psi[1](t) < Pi/2

I guess that I don't use properly the "assume" function.

The result that I would like to obain is quiet simple :

gamma0(t)) = gamma[1](t)-theta[1](t)-psi[1](t)

Thanks a lot for your help

 

Hello,

I have still some difficulties to conduct some specific trigonometric simplications but which are very common in mechanism study.

The equations are in the form :

sin(gamma0(t))*cos(beta0(t)) = -(sin(psi[1](t))*cos(theta[1](t))*cos(gamma[1](t))+sin(psi[1](t))*sin(theta[1](t))*sin(gamma[1](t))-cos(theta[1](t))*cos(psi[1](t))*sin(gamma[1](t))+cos(psi[1](t))*sin(theta[1](t))*cos(gamma[1](t)))*cos(beta[1](t))

I would like to obtain this equation after simplifications :

sin(gamma0(t))*cos(beta0(t)) = cos(beta[1](t))*sin(gamma[1](t)-theta[1](t)-psi[1](t))

I try to make a procedure to automatize the simplification of this kind of trigonometric equation.

Strangely, I noticed that the simplification is done only if there is a minus before the combine function. The simplification works but the result is wrong because i didn't obtain the good sign.

For you information, I try to make these simplifications with MMA and the FullSimplify function of MMA gives directly the expected result that is to say :

I'm sure that it shoud exist a good way to conduct this kind of simplications in Maple.

Can you help me to correct my procedure so to obtain the good result and be enough general, adaptative ? 

Code here and attached in this post :

Initialisation
restart:
with(LinearAlgebra):
with(Student[MultivariateCalculus]):
with(plots):
with(MathML):
with(ListTools):
constants:= ({constants} minus {gamma})[]:
`evalf/gamma`:= proc() end proc:
`evalf/constant/gamma`:= proc() end proc:
unprotect(gamma);
Angular Constraint equations
eq_liaison:=sin(gamma0(t))*cos(beta0(t)) = -(sin(gamma[1](t))*sin(psi[1](t))*sin(theta[1](t))-sin(gamma[1](t))*cos(theta[1](t))*cos(psi[1](t))+cos(gamma[1](t))*sin(psi[1](t))*cos(theta[1](t))+cos(gamma[1](t))*cos(psi[1](t))*sin(theta[1](t)))*cos(beta[1](t)); 
Traitement
TrigoTransform2:= proc(Eq)
local S,S1,tt,pp,Eq2,ListVariables,ListVariablesMod,Subs,size,rhsEq2,lhsEq2;
#Construit une liste à plat#
ListVariables:=indets(Eq, function(identical(t)));
ListVariables:=[op(ListVariables)];
ListVariablesMod:=map(f->cat(op(0,f),_),ListVariables);
Subs:=ListVariables=~ListVariablesMod;
#Variables Changement#
Eq2:=Eq:
print("Equation traitée=",Eq2): 
Eq2:=subs(Subs, Eq2);
print("Equation après subs=",Eq2): 
#Trigonometric transformations#
lhsEq2:=applyrule([
cos(u::anything)*cos(v::anything)-sin(u::anything)*sin(v::anything)=cos(u+v), 
cos(u::anything)*sin (v::anything)+sin(u::anything)*cos(v::anything)=sin(u+v), 
sin(u::anything)*sin(v::anything)-cos(u::anything)*cos(v::anything)=-cos(u+v), 
-sin(v::anything)*cos(u::anything)-sin(u::anything)*cos(v::anything)=-sin(u+v)], simplify(lhs(Eq2), size));
print("Equation lhsEq2 première analyse=",lhsEq2):
rhsEq2:=applyrule([
cos(u::anything)*cos(v::anything)-sin(u::anything)*sin(v::anything)=cos(u+v), 
cos(u::anything)*sin (v::anything)+sin(u::anything)*cos(v::anything)=sin(u+v), 
sin(u::anything)*sin(v::anything)-cos(u::anything)*cos(v::anything)=-cos(u+v), 
-sin(v::anything)*cos(u::anything)-sin(u::anything)*cos(v::anything)=-sin(u+v)], simplify(rhs(Eq2), size));
print("Equation rhsEq2 première analyse=",rhsEq2):
try
lhsEq2:=(trigsubs(2*combine(lhsEq2))[])/2;
print("Equation lhsEq2=",lhsEq2):
catch:
lhsEq2:=lhs(Eq2);
end try;
try
rhsEq2:=(trigsubs(-2*combine(rhsEq2))[])/2;
print("Equation rhsEq2=",rhsEq2):
catch:
rhsEq2:=rhs(Eq2);
end try;
Eq2:= lhsEq2=rhsEq2;
#Variables Changement#
Eq2:=subs(map(t->rhs(t)=lhs(t),Subs),Eq2) 
end proc:
TrigoTransform2(eq_liaison);

TrigoTransformEqAng2_anglais.mws

Thanks a lot for your help.

I don't know if I am doing it right or not because Maple isn't solving the equation. The equation solution is x=2^(1/2).

Here I let a picture of which equation I want to solve and Maple's response.

Trigonometric Equation

So it looks like radians work.

Why does degrees fail and how do I get degrees work?

How do you guys like to access pi? Do you keep a symbol of it around in a random document to open? 

 

http://i.imgur.com/07o1dyH.png

Let A(x , 2 , -1) ,B(0, y , 1) ,C(3 , 4 , -2) , AB=AC and ABC is isosceles right triangle. Find x and y ?

I am attempting to plot an initial value problem in Maple 18.  I have my equation defined, as well as a general solution and two particular solutions at y(0)=3/4 and y(0)=1/2.  To graph, I entered the command

DEplot(de,y(x),x=-3..3,{[0,1/2],[0,3/4]},dirgrid=[12,12],color=black,linecolor=blue,thickness=2);

but instead of returning a graph, the software gave me the error message

Error, (in DEtools/DEplot/CheckDE) extra unknowns found: sinx

The Maple support site lists this as an unknown error, and as a new user, I'm not sure what to do.  What does this mean?

Hello

 

I have this kind of expression :

exppr

I would like to keep a sum like and simplify all the expressions of
the type $z+\bar{z}=2Re(Z)$

 

Thanks for your suggestion

True of False, Explain:

If ∏/2<θ<∏, Then cos θ/2<0

Find the value: P=sin(10)sin(30)sin(50)...sin(890) ?

How do you express sin(4x)^2 in terms of powers of cos(x) in Maple 17?

My question is in the title, here is simple example: 

K:=(sin^2(a+b)-sin^2(a-b))

I use formula of abridged multiplication (with help of "factor")

>factor(K)

  (sin(a+b) - sin(a-b))(sin(a+b) + sin(a-b))

Then expand:

>expand(%, trig)

  4sin(a)cos(b)cos(a)sin(b)

And all I whant now is to use double angle formula like this:

4sin(a)cos(b)cos(a)sin(b) = sin(2a)sin(2b)

I am trying to use the procedure described in the answers to this question: 

http://www.mapleprimes.com/questions/100137-Solving-Trigonometric-Equations-For

to find the solutions to sin(2*x) = 1/2 where -2*Pi <= x <= 2*Pi. After the isolve() command is issued, I get the warning that solutions may have been lost. i think the issue is the form in which Maple represents the general solution to the equation. Any ideas on how to rectify this would be greatly appreciated!

Dear friends,

I have recently been calculating a sum from this link.

The problem here is to calculate the sum sum_{n>=1} (-1)^(n+1)/(n^2+a) with a some positive real number. You probably all agree that it is preferable to express it using elementary functions from basic calculus as opposed to the Gamma, Zeta and Digamma...

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