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  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?

[1] http://en.wikibooks.org/wiki/Trigonometry/The_solution_of_cubic_equations

How to solve the equation
2^(sin(x)^4-cos(x)^2)-2^(cos(x)^4-sin(x)^2) = cos(2*x)
symbolically? The solve command produces a weird answer. Evalfing all its values, one sees
0.7853981634, -0.7853981634, 2.356194490, -2.356194490,

1.570796327 - 1.031718534 I, -1.570796327 + 1.031718534 I,

1.570796327 + 1.031718534 I, -1.570796327 - 1.031718534 I,

0.7853981634, -0.7853981634, 2.356194490, -2.356194490,

1.570796327 - 1.031718534 I, -1.570796327 + 1.031718534 I,

1.570796327 + 1.031718534 I, -1.570796327 - 1.031718534 I


The identify command
interprets the real solutions on -Pi..Pi as -3*Pi/4, -Pi/4, Pi/4, 3*Pi/4
(for example,
identify(2.356194490);

3*Pi/4 ).
Is it possible to obtain these with Maple in a simpler way?

PS. Mathematica 10 does the job.

PPS. So does even Mathematica 7.

Is it possible to find all the solutions of the equation

abs(tan(x)*tan(2*x)*tan(3*x))+abs(tan(x)+tan(2*x)) = tan(3*x)

which belong to the interval 0..Pi with Maple?

 

 

eq1:=
(1/4)*D^2*Pi-(1/4)*D^2*arccos((-D+2*h)/D)-(1/2)*sqrt(h)*sqrt(D-h)*D+h^(3/2)*sqrt
(D-h);
                          
eq2 :=
-(1/2)*sqrt(h)*sqrt(D-h)*D+h^(3/2)*sqrt(D-h)+(1/4)*D^2*arcsin((-D+2*h)/D)+(1/8)*
D^2*Pi;

These equations are the same. yet simplify(eq1-eq2,trig);
<>0
The Mathematica COMMAND FullSimplify[..] gets zero.

How to calculate mul(sqrt(3)+tan((1/180)*Pi*j), j = 1 .. 29) exactly?
The command
simplify(mul(sqrt(3)+tan((1/180)*Pi*j), j = 1 .. 29), trig)
is spinning.

A reddit user posted an interesting question:

http://www.reddit.com/r/math/comments/1eyx0f/help_with_simplifying_in_maple/

The problem is how to simplify, e.g. 2/3*37^(1/2)*sin(1/6*Pi+1/3*arccos(55/1369*37^(1/2)))+2/3 to 4.  I tried a few things and got nowhere.  Any suggestions?

Hi,

with great interest and surprise I read the post
"Converting Half-Angle Trig Formulas to Radicals".
Isnt it possible to evaluate cos(arccos(13/14)/3) also
to an exact expression in radicals ?
I simply do not succeed with my humble knowledge of
the Maple commands/internal workings...
Would be great if someone finds a solution ( of an 
unsolvable problem ??? ).

[Edit: Excess white space deleted.---Carl Love]

Hi,

I have a trigonometric series which contains 1D and 2D modes. It looks something like the following:

S:= Acos(mx)sin(nz) + Bcos(kz)sin(qx) + Csin(sz) for m,n,k,q,s=1,.....10.

I am iterested in obtaining the amplitudes of the 1D modes (i.e. C in the above expression). Is there a way to do this using the coeffs function? I would like to use this in such a way as to isolate the 1D modes from th series. Any suggestions?

 

Thanks for your help.

I am using the function solve() to find roots of a trig. equation. Such as for sin(k*x) = 0, Maple retuns x = 0, whereas I expecting to get  x = n ∏/k, for n = 0,1,2,.... I am sorry I am new to Maple, can anyone help me get what I am looking for?

Thank you

Sorry, this seems like a silly question. But is there an easy way to convert trig funcitons, or even non trig functions to orthogonal (in this case Legendre) polynomials? 

Hello!

if anyone can help ill be greatful!.

i have his equation:

eq1:=(8/x)=tan(7*x/50)

of course  there are infinite analitical solutions....   solution = F(x)+Pi*n, n=1....infinity

what i want to do, is to define N. and then,  to put the first N solutions of the equation into a Vector called X,

so X[1]=F(x)+1*Pi

X[2]=F(x)+2*Pi

...

X[N]=F(x)+N*Pi

can someone help?

I have a problem with inputting a new package in my version of maple (15) for mac. The packes makes it possible to do calculations with cos/sin/tan in degrees instead of radians. I need to use this for my Engeneering studies in Denmark.

In pc you just place the package in the labrary subfolder under the Maple 15 folder, but i can't find that subfolder anywhere on my mac??
Where should i put the package to make it work?

I have 2 files; "Trig.ind" and "Trig.lib" - whichone to use?

for example:

>>simplify(cos(i)*sin(u)/sin(i),trig)

                    cos(i)*sin(u)/sin(i)

Maple do'not  simplify cos(i)/sin(i)=ctan(i) atomaticly.

also  half angle formulas:

>>simplify(sin(i)/(cos(i)+1),trig)

           sin(i)/(cos(i)+1)

i want to get tan(i/f)

Hi All,

 

I am using maple 15 for a mechanical modeling, which has some very complex trigonomitry manipulations. The

script runs fine in maple 9.5.1 under window XP. But when I try to load the script in maple 15 under window 7,

it keeps loading forever. I noticed the memory usage in window manager to approach 1GB. (I have 4 GB in my PC).

The 9.5.1 uses much small portion of the memory. Does anyone see this problem before?

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