How to solve advanced algebra equation with multiple variables?

In summary, the conversation is about solving an algebra equation involving multiple variables and trigonometric functions. The goal is to find θ1, θ2, and θ3 in terms of x, y, z, and p. The poster suggests using exponential and t-formulas to simplify the problem but has not been successful in solving it. They ask for help from anyone who is able to solve the equation.
  • #1
ohaiyo88
12
0

Homework Statement


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

Homework Equations


cosθ23 = cos(θ23)
sinθ23 = sin(θ23)

Finding θ123. 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..
 
Last edited:
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  • #2
What is it that you want to do? Do you want to express [itex]l_1,l_2,l_3[/itex] in terms of [itex]x,y,z[/itex] and [itex]\theta_1,\theta_2,\theta_3[/itex]?

Your notation is kind of hard to follow. This post explains how you can make your math look nice.
 
  • #3
Find θ1,θ2,θ3 in terms of x,y,z and p. Sorry for the inconvenience.
 
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  • #4
Uuuh, perhaps you should try a numerical solution...

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

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

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:

[tex]\sin(\theta_i)=\frac{2t_i}{1+t_i^2},~\cos(\theta_i)=\frac{1-t_i^2}{1+t_i^2}[/tex]

with [itex]t_i=\tan(\theta_i/2)[/itex]

This puts the sines and cosines in the same variable. This might be easier to solve. I guarantee nothing however...
 
  • #5
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.
 
  • #6
Anyone here can lend a golden hand?
 

What is advanced algebra?

Advanced algebra is a branch of mathematics that deals with more complex equations and functions, including polynomials, logarithms, and trigonometric functions.

What are some real-life applications of advanced algebra?

Advanced algebra is used in a variety of fields, including physics, engineering, economics, and computer science. Some common applications include modeling complex systems, optimizing processes, and analyzing data.

What are some common techniques used in advanced algebra?

Some common techniques used in advanced algebra include factoring, completing the square, and using logarithms and exponential functions to solve equations.

What is the difference between advanced algebra and basic algebra?

The main difference between advanced algebra and basic algebra is the complexity of the equations and functions being studied. Advanced algebra deals with more abstract and complex concepts, while basic algebra focuses on fundamental concepts such as solving equations and graphing linear functions.

Why is it important to study advanced algebra?

Studying advanced algebra helps develop critical thinking and problem-solving skills that are applicable in many areas of life. It also provides a foundation for higher-level math courses and is necessary for many STEM fields.

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