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2 Trigonometric function with two unidentified

SOLVED
Regular Member

2 Trigonometric function with two unidentified

Hello guys, I am stuck for two days about an issue. I have to create a solution matrix for the following two trigonometric functions.

m*cos(a)+n*cos(b)=x

m*sin(a)+n*sin(b)=y

 

0<a<180 , 0<b<180

m,n,x,y are constants. a,b are unidentified.

How can I solve x,y as matrix solution?

 

I will trigger x,y values with FRAME, so at each X.i, Y.i values I have to calculate a,b degrees and draw lines.

I am using MathCAD 15.

I would really appreciate your help. Thanks in Advance!

 

1 ACCEPTED SOLUTION

Accepted Solutions

Re: 2 Trigonometric function with two unidentified

If you limit Theta2, too (positive in the range from 0 to 180°) you have a unique, single solution.

One way to calculate the angles Theta1 and Theta2 based on the coordinates x,y of the endpoint is shown in the picture below:

B.png

B2.png

22 REPLIES 22

Re: 2 Trigonometric function with two unidentified

You would like to create an animation if you use the FRAME variable?

Let us create one frame of this animation!

 

Re: 2 Trigonometric function with two unidentified

Thank you for your intention @ValeryOchkov 

 I'll show with sketch in add.

 

There is K.i matrix. It consists nodes that arm going to reach. Arms are should be rectangular boxes. I wrote the translational and rotational matrix. Arms are working perfrectly fine. But it needs target node in order to calculate teta1 and alpha angles.

For example K.1 is (x,y)=(450,600)

It will calculate these angles then will go to K.2=(460,590), later on K.3=(465,582) and so on.

 

I will later make K.i matrix with bezier if I can finish this earlier. It has manual nodes added by me now.

I hope I could explained myself clearly. Thank you!

 

Re: 2 Trigonometric function with two unidentified

May be so

 

Re: 2 Trigonometric function with two unidentified

Hi,

The analytical solution gives me these results:

Solution11.jpg

Re: 2 Trigonometric function with two unidentified

When a function with sin and cos, it's easier to make matrix solution. However in my function, there are only cos or sin one function Smiley Sad. I have to make a general matrix solution. I am sorry I couldn't understand by your point. What do you suggest me to do exactly. I need this kind of solution below:

DSC_0658.JPGSin-cos

Re: 2 Trigonometric function with two unidentified

Solution12.jpg

Re: 2 Trigonometric function with two unidentified

Thank you really but I gave it as an example. The actual functions I ask are in The main post. I know this one...

Re: 2 Trigonometric function with two unidentified

see please the attach

sincos.gif

Re: 2 Trigonometric function with two unidentified

Solution13.jpg