SOLUTION: I have to resolve the equation in the interval 0 &#8804; Ø < 2x. sin Ø = &#8730;2 - cos Ø

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Question 1035765: I have to resolve the equation in the interval 0 ≤ Ø < 2x. sin Ø = √2 - cos Ø
Found 2 solutions by fractalier, Alan3354:
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
By looking at it, I can see that the angle needed is 45 degrees...to verify it, I went and graphed
y+=+sin%28x%29+%2B+cos%28x%29+
and found that the graph only reaches sqrt(2) at 45 degrees...

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
sin Ø = sqrt(2) - cos Ø
sin^2 = 2 - sqrt(8)cos + cos^2
1 - cos^2 = 2 - sqrt(8)cos + cos^2
2cos^2 - sqrt(8)cos + 1 = 0
disc = b^2 - 4ac = 8 - 8 = 0
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cos = -b/2a = 2sqrt(2)/4 = sqrt(2)/2
Ø = pi/4, 0< Ø < 2pi (not 2x)