Items tagged with angle

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How to get tangent angle between two curves? 

example for these : f(x)=((x^4+5)^(1/2))/(sinx+5) and g(x)=cosx^2   ; x>0

thanks :)

Dear readers,

For a question for my students I want them to calculate tge resulting vector from two vectors. The student had to answer by giving the length and angle of the resulting vector.

For the question the vector angle is always larger as 180 derges, the student should for example give a result of 270 degrees.

Currently I'm using the following code:

$F1=100;#range(200,500,20);
$F2=100;#range(100,200,10);
$A1=45;#range(10,80,5);
$A2=45;#range(10,80,5);
$A1r=180+$A1;
$A2r=360-$A2;
$F1x=maple("cos(($A1r)*Pi/180)*$F1");
$F1y=maple("sin(($A1r)*Pi/180)*$F1");
$F2x=maple("cos(($A2r)*Pi/180)*$F2");
$F2y=maple("sin(($A2r)*Pi/180)*$F2");
$V1=maple("Vector(2,[($F1x),($F1y)])");
$V2=maple("Vector(2,[($F2x),($F2y)])");
$V3=maple("($V1)+($V2)");
$F3=maple("LinearAlgebra[Norm]($V3)");
$V0x=maple("Vector(2,[1,0])");
$A3=maple("LinearAlgebra[VectorAngle](($V0x),($V3))");
$A4=maple("evalf((($A3)*180/(Pi)))");

As you can see maple will always give an angle smaller than 180 degrees since the angle between two vectors is always 180 degrees or smaller.

Can anyone tell me how I should code this problem such that the rest for A4 will be 270 degrees rather than 90 degrees, as is given from the current way of coding.

Thank you in advance.

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

Hi,

I would like to plot a cone where I can change the vertex angle directly. I would also to be able to change the size of the cone. I have tried:

cone([r*cos(phi)*sin(theta), r*sin(phi)*sin(theta), r*cos(theta)], phi = 0 .. 2*Pi, r = 0 .. 1, theta = (1/6)*Pi, coords = spherical)

but this gives me the following error:

Error, (in plot3d) unexpected options: [[r*cos(phi)*sin(theta), r*sin(phi)*sin(theta), r*cos(theta)], phi = 0 .. 2*Pi, r = 0 .. 1, theta = (1/6)*Pi]

Thanks!

Hei, I'm trying to create a random walk in the plane, with constant step length (=1) and the angle between two consecutive steps are decided by a probability density function. I just can't seem to find out how I should implement the density function into my worksheet.

The probability density function is: p(phi)=(1/4)*cos(phi/2), on the interval [-Pi,Pi].
And  I think i managed to do it by selecting a random angle, but don't know how to generate a random angle given this probability function. Any ideas? It'd be highly appreciated!


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