Advanced Algebra Question

[ohaiyo88]

Homework Statement

x= cosθ₁p₃(cosθ₂₃)+cosθ₁(cosθ₂p₂-a)-sinθ₁p₁
y= sinθ₁p₃(cosθ₂₃)+sinθ₁(cosθ₂p₂-a)+cosθ₁p₁
z= sinθ₂₃p₃-sinθ₂p₃

Homework Equations

cosθ₂₃ = cos(θ₂ +θ₃)
sinθ₂₃ = sin(θ₂ +θ₃)

Finding θ₁,θ₂,θ₃. Solve in terms of x,y,z,p
Pls help to solve this algebra equation by eliminating the variable. Thanks in advance for the helping..im doing my final year project and came across to this unsolvable problem..

 

[Fredrik]

What is it that you want to do? Do you want to express $l_1,l_2,l_3$ in terms of $x,y,z$ and $\theta_1,\theta_2,\theta_3$?

Your notation is kind of hard to follow. This post explains how you can make your math look nice.

 

[ohaiyo88]

Find θ1,θ2,θ3 in terms of x,y,z and p. Sorry for the inconvenience.

 

[micromass]

Uuuh, perhaps you should try a numerical solution...

If you don't want that, then you can always try to use

$$\cos(x)=\frac{e^{ix}+e^{-ix}}{2}~\text{and}~\sin(x)=\frac{e^{ix}-e^{-ix}}{2i}$$

This turns the geometric problem into an exponential problem which might be easier to solve.

Another thing you should consider are the t-formula's:

$$\sin(\theta_i)=\frac{2t_i}{1+t_i^2},~\cos(\theta_i)=\frac{1-t_i^2}{1+t_i^2}$$

with $t_i=\tan(\theta_i/2)$

This puts the sines and cosines in the same variable. This might be easier to solve. I guarantee nothing however...

 

[ohaiyo88]

but i tried both methods, it just make the question more complicated than ever. I used to squaring up x and y, and add both together, I am sucessfully eliminate θ1, but others seems to have trouble.

 

[ohaiyo88]

Anyone here can lend a golden hand?