Items tagged with trig

I have in mind all the real roots of the equation 2*tan(Pi*t^2)-tan(Pi*t)+tan(Pi*t)*tan(Pi*t^2)^2 = 0.

Maple fails with it:

>RealDomain:-solve(2*tan(Pi*t^2)-tan(Pi*t)+tan(Pi*t)*tan(Pi*t^2)^2 = 0, t);


 Even its numerical solution has gaps.

>Digits := 15; a := Student[Calculus1]:-Roots(2*tan(Pi*t^2)-tan(Pi*t)+tan(Pi*t)*tan(Pi*t^2)^2 = 0, t = -2 .. 2);
Warning, some roots are returned as numeric approximations
 [-1.35078105935821, -1.18614066163451, -1.00000000000000, 0, 

   1.00000000000000, 1.28077640640442, 1.68614066163451,    1.85078105935821]



>b := Student[Calculus1]:-Roots(2*tan(Pi*t^2)-tan(Pi*t)+tan(Pi*t)*tan(Pi*t^2)^2 = 0, t = -2 .. 2, numeric);
 [-1.35078105935821, -1.18614066163451, -1.00000000000000, 

   -0.780776406404415, 0., 1.00000000000000, 1.28077640640442, 

   1.68614066163451, 1.85078105935821, 2.00000000000000]


>plot(2*tan(Pi*t^2)-tan(Pi*t)+tan(Pi*t)*tan(Pi*t^2)^2, t = -2 .. 2);

shows 14 solutions.

The output of the command


[1/4-(1/4)*sqrt(41), 1/4-(1/4)*sqrt(33), -1, 0, 1, 1/4+(1/4)*sqrt(17), 1/4+(1/4)*sqrt(33), 1/4+(1/4)*sqrt(41)]

suggests a closed-form expression for the roots.

N := 4;
print(`output redirected...`); # input placeholder
y := sum(A[2*n].cos(2.*n.x), n = 0 .. N);

eq1 := diff(y, `$`(x, 2))+(a+2*q*cos(2*x))*y

eq2 := map(combine, eq1, trig)

for i from 0 to 4 do eq4[i] := coeff(eq2, cos(2*n*x)) end do

From these I want to extract the co-ffficients of cos(0x),cos(2x),cos(4x)..

and form a simultaneous linear equation containg A0,A2,A4

The solution is 



Can anybody tell me how to do it

Hi folks,

I've come across this project which involves large algebraic expressions and I need to be able to simplify it using Maples in-built features, but with no succes.

The problem involves trig-functions. For instance I have several expressions involving:

       cos(v)*sin(w)-cos(w)*sin(v)       which I know equals     -sin(v-w)

but even if I use simplify, trig, size and so on it won't apply the above identity. Btw there are several other identities that aren't applied either.

Is there any way to "force" the above identity into consideration??



I am having issue in finding the explanation on how to solve inverse trig funtion and expression with inverse trig funtions. I do not understand my school book and I was hoping that the software would have given me an extra help in understanding my school problems. 


Thank you very much


Perla D'andrea


After trigonometric manipulations in a mechanical problem, I can obtain the desired angles but defined with modulo 2Pi.

I would like to program or find a function which can do this operation :

While angle doesn't belong to [-Pi, Pi]


  If angle > Pi then do angle = angle - 2Pi

  If angle < - Pi then do angle = angle + 2Pi


Is there an existing function which can do this operation ?

Otherwise, may you help me to program it ?

Thanks a lot for your help


I would like to simplify a trigonometric equation that I obtain with a vectorial closure (in mechanics)

Here the equation that I would like to simplify 

eq_liaison := (-sin(p(t)+g(t))*cos(a(t))-sin(b(t))*sin(a(t))*cos(p(t)+g(t)))*l2[1]+((-sin(p(t)+g(t))*cos(a(t))-sin(b(t))*sin(a(t))*cos(p(t)+g(t)))*cos(th(t))+(-cos(p(t)+g(t))*cos(a(t))+sin(a(t))*sin(b(t))*sin(p(t)+g(t)))*sin(th(t)))*l3[1]+(-sin(a(t))*sin(g(t))*sin(b(t))+cos(a(t))*cos(g(t)))*xb[1]+sin(a(t))*cos(b(t))*yb[1]+(sin(a(t))*sin(b(t))*cos(g(t))+cos(a(t))*sin(g(t)))*zb[1]+x(t)-xp(t) = 0

Do you have ideas so as to simplify again this expression ?

This expression can still be simplified. You can find here the result expected :


I find surprising that I have so many difficulties to make trigonometric simplications with the trigonometric functions.

I attached the code 


Thank you for your help

I have:




then I tried:

spacecurve(r(t), t = 0 .. 2*Pi, thickness = 2, color = black, axes = normal, labels = [x, y, z], numpoints = 150)

But I keep getting the error: Warning, unable to evalute the function to numeric values in the region. 

But I thought <4cos2t+4sint, 5cos3t+4cost, (sin3t+2sint)^2> was defined on the region t=0 to 2Pi??? 

I'm using Maple 2015 if that helps. 


here a comlicated formula,how i simplify

thanks  a lot.


f := (kappa*omega^2+omega^3)*(Y+(-sqrt(N)*omega^(3/2)*sin(theta[2])*cos(varphi[2])*lambda__b+sqrt(N)*omega^(3/2)*sin(theta[1])*cos(varphi[1])*lambda__a)/(2*(kappa*omega^2+omega^3)))^2/(2*omega)+(-kappa*omega^2+omega^3)*(X+(sqrt(N)*omega^(3/2)*sin(theta[2])*cos(varphi[2])*lambda__b+sqrt(N)*omega^(3/2)*sin(theta[1])*cos(varphi[1])*lambda__a)/(2*(-kappa*omega^2+omega^3)))^2/(2*omega)+(Omega*N*cos(theta[2])*omega+Omega*N*cos(theta[1])*omega-P__X^2*kappa+P__X^2*omega+P__Y^2*kappa+P__Y^2*omega)/(2*omega)-(sqrt(N)*omega^(3/2)*sin(theta[2])*cos(varphi[2])*lambda__b+sqrt(N)*omega^(3/2)*sin(theta[1])*cos(varphi[1])*lambda__a)^2/(8*omega*(-kappa*omega^2+omega^3))-(-sqrt(N)*omega^(3/2)*sin(theta[2])*cos(varphi[2])*lambda__b+sqrt(N)*omega^(3/2)*sin(theta[1])*cos(varphi[1])*lambda__a)^2/(8*omega*(kappa*omega^2+omega^3))







    f is a complicated function,i want to make it more simplify,but i want to keep square style,

 let coefficients of X and Y keep one unit,and simplify terms  containd special symbol of omega



it what i wanted.

I want to reduce all solution of the equation sin(x)^2=1/4

sol:=solve(sin(x)^2=1/4, x, AllSolutions);


sol:=solve(k=1/4, x, AllSolutions = true, explicit);

How can I reduce solution sol := -1/3*Pi*_B3+1/6*Pi+Pi*_Z3 ?

How can I get x= pi/6+k*pi and x= -pi/6+k*pi?

Hi guys.

I want to know how can I make the maple to give final response of a simple trigonometric function, e.g sin(pi/6). When I type sin(pi/6) in the command line and then press enter, maple give the same, I mean sin(pi/6) at the next line. I want 0.5 as the final response not sin(pi/6) again. Simplify command does not work for me in this case.

Thanks in advance.

When I do simplify(LegendreP(n, 1, cos(t))), Maple gives me -sqrt(1-cos(t))*sqrt(cos(t)+1). Isn't it the same thing as -sin(t)? How can I have Maple further convert/simplify it to -sin(t)? (I tried simplify(%, trig) but it didn't work). I am new on Maple. Thanks in advance for anyone's help!


I'm looking at Maple as a possible alternative to Mathcad (which I've been using for years, but is now very jaded compared to other options like Maple and Mathematica).  I'm a civil engineer and for what I do, one of the better features of Mathcad is the way it handles units.  For example, if I specify an angle in degrees (say phi=30 degrees) and then ask for sin(phi), I get 0.5.  At face value, I though Maple would do the same kind of thing.  However, this doesn't appear to be the case (see attached worksheet).  The only workaround that I can see is to specify the angle in degrees (but without assigning ) and then multiply the specified value by pi/180 (to convert to radians) before passing it to the sin function.  Which is all a bit messy and not at all an attractive solution.

Am I misunderstanding the way units work in Maple and is there a clean way of specifying angles in degrees (which is what engineers work with) and using these values directy in trig functions?

Thanks in anticipation,


  Solving trigonometry Equations  sin^2(2x)-cos^2(8x)=0.5cos(10x)

There are two ways of expressing the solution to a cubic equation, one of them uses cos and arccos [1]. How do I / is there a way to ask Maple to get this form?

More generally, can Maple be instructucted to solve equations using trig identities?


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