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Simplifying 3cos(x + -10) + 4sin(x + 40) = 0 Reorder the terms: 3cos(-10 + x) + 4sin(x + 40) = 0 (-10 * 3cos + x * 3cos) + 4sin(x + 40) = 0 (-30cos + 3cosx) + 4sin(x + 40) = 0 Reorder the terms: -30cos + 3cosx + 4ins(40 + x) = 0 -30cos + 3cosx + (40 * 4ins + x * 4ins) = 0 -30cos + 3cosx + (160ins + 4insx) = 0 Solving -30cos + 3cosx + 160ins + 4insx = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-160ins' to each side of the equation. -30cos + 3cosx + 160ins + -160ins + 4insx = 0 + -160ins Combine like terms: 160ins + -160ins = 0 -30cos + 3cosx + 0 + 4insx = 0 + -160ins -30cos + 3cosx + 4insx = 0 + -160ins Remove the zero: -30cos + 3cosx + 4insx = -160ins Add '-4insx' to each side of the equation. -30cos + 3cosx + 4insx + -4insx = -160ins + -4insx Combine like terms: 4insx + -4insx = 0 -30cos + 3cosx + 0 = -160ins + -4insx -30cos + 3cosx = -160ins + -4insx Reorder the terms: -30cos + 3cosx + 160ins + 4insx = -160ins + 160ins + -4insx + 4insx Combine like terms: -160ins + 160ins = 0 -30cos + 3cosx + 160ins + 4insx = 0 + -4insx + 4insx -30cos + 3cosx + 160ins + 4insx = -4insx + 4insx Combine like terms: -4insx + 4insx = 0 -30cos + 3cosx + 160ins + 4insx = 0 Factor out the Greatest Common Factor (GCF), 's'. s(-30co + 3cox + 160in + 4inx) = 0Subproblem 1
Set the factor 's' equal to zero and attempt to solve: Simplifying s = 0 Solving s = 0 Move all terms containing c to the left, all other terms to the right. Add '-1s' to each side of the equation. s + -1s = 0 + -1s Remove the zero: 0 = -1s Simplifying 0 = -1s The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-30co + 3cox + 160in + 4inx)' equal to zero and attempt to solve: Simplifying -30co + 3cox + 160in + 4inx = 0 Solving -30co + 3cox + 160in + 4inx = 0 Move all terms containing c to the left, all other terms to the right. Add '-160in' to each side of the equation. -30co + 3cox + 160in + -160in + 4inx = 0 + -160in Combine like terms: 160in + -160in = 0 -30co + 3cox + 0 + 4inx = 0 + -160in -30co + 3cox + 4inx = 0 + -160in Remove the zero: -30co + 3cox + 4inx = -160in Add '-4inx' to each side of the equation. -30co + 3cox + 4inx + -4inx = -160in + -4inx Combine like terms: 4inx + -4inx = 0 -30co + 3cox + 0 = -160in + -4inx -30co + 3cox = -160in + -4inx The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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