Sin x + 22 degrees equals cos 2x - 7 degrees

sin22 = 0.375
cos7 = 0.993

cos2x = 1 - 2sin^2x

solve like a regular quadratic by completing the square: 2sin^2x + sinx = 0.632
2sin^2x + sinx - 1 = 0.632 - 1
(2sinx - 1)(sinx + 1) = -0.368

2 possible solutions:

1) 2sinx - 1 = -0.368
2sinx - 1 +1 = -0.368+1
2sinx = 0.632
2sinx/2 = 0.632/2
sinx = 0.316
x = sin^-1 (0.316) = 18.42

2) sinx + 1 = -0.368
sinx + 1 -1 = -0.368-1
sinx = -1.368
x = sin^-1 (-1.368) = UNDEFINED

Therefore x = 18.42

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