How to show this Q&A on Maple...

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How can i answer iv on Maple?

New to maple. How to simplify result?...

Asked by:

Hello,

I've just started to use Maple 16, and I can't seem to get a neat result, when I use the solve function to solve 4 equations with 4 unknown constants.

I've posted my calculations.

How can I get a simpler result? I found a simplification command, but that didn't help

How to solve this trig equation?...

Asked by:

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);

RootOf(tan(_Z)*tan(_Z^2/Pi)^2-tan(_Z)+2*tan(_Z^2/Pi))/Pi```

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]

>nops(a);

8

>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]
>nops(b);
10```

whereas

`>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

```>identify(a);

[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.

Coefficients extraction to form Equations...

Asked by:

N := 4;
print(`output redirected...`); # input placeholder
4
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

aA0+qA2=0

2q*A0+(a-4)*A2+q*A4=0

Can anybody tell me how to do it

How to simplify this?...

Asked by:

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??

expression with inverse trig funtion...

Asked by:

Hello

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

Regards,

Perla D'andrea

How to determine an angle in [-Pi,Pi]?...

Asked by:

Hello,

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]

do

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

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

end

Is there an existing function which can do this operation ?

Otherwise, may you help me to program it ?

Thanks a lot for your help

Simplification of trigonometric equations. V...

Asked by:

Hello,

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

Error when plotting spacecurve...

Asked by:

I have:

r:=t-><4cos2t+4sint,5cos3t+4cost,(sin3t+2sint)^2>

with(plots):

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.

How to simplify certain terms of it?...

Asked by:

hi,

here a comlicated formula,how i simplify

thanks  a lot.

 >
 (1)
 >
 (2)
 >

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

Download Q1119.mw

it what i wanted.

Asked by:

How can I reduce all solutions ?...

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

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

and

restart:
k:=combine((sin(x))^2);
sol:=solve(k=1/4, x, AllSolutions = true, explicit);
simplify(sol);

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?

Calculation of trigonometric function...

Asked by:

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.

How can I simply the trig functions in expansion o...

Asked by:

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!

Using angular units with trig functions...

Asked by:

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,

Ian

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