I can't remember how to solve these. Any help? I tried using Euler's formula, no avail.
sin(x)+sin(y) = 0.90154195
cos(x)+cos(y) = 1.64483049
Solve for x & y:
(1) : sin(x)+sin(y) = 0.90154195
(2) : cos(x)+cos(y) = 1.64483049
(2) + i(1) : e^ix + e^iy = 1.64 + i0.90
(2) - i(1) : e^-ix + e^-iy = 1.64 - i0.90
Now use A = e^ix; B = e^iy.
A + B = 1.64 + i0.90
1/A + 1/B = 1.64 - i0.90
Solve this system.
If the i is tripping you up, there is another way to solve it directly:
Square the first and second equations and add them (it simplifies very nicely with trig identities).
You will be able to solve for x - y.
Then use substitution.
I'm attempting to solve by squaring the equations and adding them. I come up with this:
sin^2(x)+2sin(x)sin(y)+sin^2(y)+cos^2(x)+2cos(x)co s(y)+cos^2(y) = (0.90)^2+(1.64)^2
since sin^2(x)+cos^2(x)=1, we have:
which simplifies as:
2+2cos(x-y) = 0.9^2 + 1.64^2
is this where you were headed? I'm not sure how to solve for x and y here though...