2 simutaneous equations from my coursework

4=4cosx+3cos(x+y)

3=4sinx+3sin(x+y)

looking for analytical solution, should yield 2 pairs of answers

Thanks in advance guys! (Clapping)

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- Jan 2nd 2010, 04:06 PMcybernoaneed help on 2 simutaneous trig. equations
2 simutaneous equations from my coursework

4=4cosx+3cos(x+y)

3=4sinx+3sin(x+y)

looking for analytical solution, should yield 2 pairs of answers

Thanks in advance guys! (Clapping) - Jan 2nd 2010, 08:40 PMpickslides
Hi there, you should consider

and

Now expand each expression out - Jan 2nd 2010, 10:10 PMbigwavethink algrebra
see soroban's solution

- Jan 2nd 2010, 10:33 PMSoroban
Hello, cybernoa!

Quote:

Looking for analytical solution, should yield 2 pairs of answers.

We have: .

. . .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Let in [2]: .

. . . .

. . . . . . . . . .

Divide by 5: . .[3]

Let: . .[4]

Substitute into [3]: .

Then we have: .

Substitute [4]: .

One solution: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Let in [2]: .

. . . .

. . . . . . . . . .

Divide by 5: . .[5]

Let: . .[6]

Substitute into [5]: .

Then we have: .

Substitute [6]: .

Another solution: .

- Jan 2nd 2010, 10:55 PMDrexel28