## Numerical solution of trigonometric equation...

how to get numerical values of the following:

cos(pi/2)^2  where square should be on cos not on angle

## How do I display the numeric value for a trig func...

when I enter a trig function as cos(pi/2) I get as a return the same input.  What I would like is the numeric answer displayed. also there are times when I don't want pi in the answer but a numeric value calculated based on pi * whatever.

Thanks

Bill

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

How can i answer iv on Maple?

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

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?...

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...

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?...

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...

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]?...

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...

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

## Error when plotting spacecurve...

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?...

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

it what i wanted.

## How can I reduce all solutions ?...

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?