Can somebody show I how to use the three equations to get the same answer for Tac and Tad? Answer for Tac=16.9 and for Tad=35.9. Please show steps so I understand.
eq1 0Tab+ -.5Tac+0.5Tad+0Wa=0
eq2 .707Tab+ -.75Tac+.75Tad+0Wa=0
eq3 .707Tab+.433Tac+.433Tad-1Wa=0
typo. It is for tab and Tac not Tad.Tab=35.9 and Tac=16.9
Rather than those tacky Ta* names, I'll just call them b,c,d
And what is that Wa name supposed to be? You say that the Ta* variables have numeric values, but that's not possible if there's a Wa variable floating about. Is that supposed to be just another name? I'll call it a. Then we have
(#1) 0b - .5c + 0.5d = 0
(#2) .707b - .75c + .75d = 0
(#3) .707b + .433c + .433d = 1
Those look suspiciously like sines and cosines. Is this some kind of rotation mattix? Anyway, since you want numeric values for b,c,d, I'll let a=1.
Subtracting #2 from #3, we are left with
(#1) -.5c + 0.5d = 0
(#4) 1.183c - 0.317d = 1
Sine #1 says that c = d, we are left with
0.866d = 1
d = 1/.866 = 2/√3
Ahhh! Now I see that Tad is supposed to mean tan(d). Why didn't you say so?
tan 40.9° = 2/√3
I do not know how you got the values you did.
I still don't know what trig function W is supposed to be, but the key to doing this is just solving as any other 3x3 matrix, for which there are numerous online calculators. In any case, once you have a value for Tac, then c = arctan(Tac)
Wa=40
Canyou show I how the matrix will like because I confuse on how to enter it on the trix calculator. If you can post the site below so I can get to it and see. I have nver use a matrix calculator before.
no idea, but surely you just enter the numbers and tell it to solve the matrix. If it's any good, it will have examples. I know wolframalpha.com solves matrices, in several ways. It has helpful examples of the syntax to use.
There are also Gauss-Jordan elimination solvers you can use. google will provide several web sites.
To find the values of Tac and Tad that satisfy all three equations, we can use the method of simultaneous equations. Here's how to solve them step by step:
Step 1: Write the equations in a matrix form.
To make it easier to solve the equations, we can rewrite them in matrix form. The matrix form of the equations is:
| 0 -0.5 0.5 0 | | Tab | | 0 |
| 0.707 -0.75 0.75 0 | x | Tac | = | 0 |
| 0.707 0.433 0.433 -1 | | Tad | | 0 |
Step 2: Solve the matrix equation.
To solve the matrix equation, we can use the Gaussian elimination method or matrix inversion. In this case, let's use Gaussian elimination.
First, let's set up the augmented matrix:
| 0 -0.5 0.5 0 | | Tab | | 0 |
| 0.707 -0.75 0.75 0 | x | Tac | = | 0 |
| 0.707 0.433 0.433 -1 | | Tad | | 0 |
Now, perform row operations to eliminate some entries:
R2 = R2 - 0.707R1
R3 = R3 - 0.707R1
The augmented matrix becomes:
| 0 -0.5 0.5 0 | | Tab | | 0 |
| 0 0.232 0.549 0 | x | Tac | = | 0 |
| 0 0.232 0.211 -1 | | Tad | | 0 |
Now, let's perform more row operations to further eliminate entries:
R3 = R3 - R2
The augmented matrix becomes:
| 0 -0.5 0.5 0 | | Tab | | 0 |
| 0 0.232 0.549 0 | x | Tac | = | 0 |
| 0 0 -0.338 -1 | | Tad | | 0 |
Step 3: Solve for Tac and Tad.
Now that the matrix equation is in row-echelon form, we can solve for Tac and Tad using back substitution.
From the bottom equation, we have:
-0.338Tad - Tac = 0
Solving for Tad, we get:
Tad = -Tac / -0.338
Substituting this value of Tad into the middle equation, we have:
0.232Tac + 0.549(-Tac / -0.338) = 0
0.232Tac + 1.624Tac = 0
1.856Tac = 0
Tac = 0
Using this value of Tac, we can substitute it back into Tad = -Tac / -0.338:
Tad = -0 / -0.338
Tad = 0
Therefore, Tac = 0 and Tad = 0 satisfy all three equations.
Please note that the values you provided for Tac=16.9 and Tad=35.9 do not satisfy the equations.