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Simplifying Sin(4x + 30) = cos(-2x + 54) Reorder the terms: inS(30 + 4x) = cos(-2x + 54) (30 * inS + 4x * inS) = cos(-2x + 54) (30inS + 4inxS) = cos(-2x + 54) Reorder the terms: 30inS + 4inxS = cos(54 + -2x) 30inS + 4inxS = (54 * cos + -2x * cos) 30inS + 4inxS = (54cos + -2cosx) Solving 30inS + 4inxS = 54cos + -2cosx Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Reorder the terms: -54cos + 2cosx + 30inS + 4inxS = 54cos + -2cosx + -54cos + 2cosx Reorder the terms: -54cos + 2cosx + 30inS + 4inxS = 54cos + -54cos + -2cosx + 2cosx Combine like terms: 54cos + -54cos = 0 -54cos + 2cosx + 30inS + 4inxS = 0 + -2cosx + 2cosx -54cos + 2cosx + 30inS + 4inxS = -2cosx + 2cosx Combine like terms: -2cosx + 2cosx = 0 -54cos + 2cosx + 30inS + 4inxS = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-27cos + cosx + 15inS + 2inxS) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-27cos + cosx + 15inS + 2inxS)' equal to zero and attempt to solve: Simplifying -27cos + cosx + 15inS + 2inxS = 0 Solving -27cos + cosx + 15inS + 2inxS = 0 Move all terms containing i to the left, all other terms to the right. Add '27cos' to each side of the equation. -27cos + cosx + 15inS + 27cos + 2inxS = 0 + 27cos Reorder the terms: -27cos + 27cos + cosx + 15inS + 2inxS = 0 + 27cos Combine like terms: -27cos + 27cos = 0 0 + cosx + 15inS + 2inxS = 0 + 27cos cosx + 15inS + 2inxS = 0 + 27cos Remove the zero: cosx + 15inS + 2inxS = 27cos Add '-1cosx' to each side of the equation. cosx + 15inS + -1cosx + 2inxS = 27cos + -1cosx Reorder the terms: cosx + -1cosx + 15inS + 2inxS = 27cos + -1cosx Combine like terms: cosx + -1cosx = 0 0 + 15inS + 2inxS = 27cos + -1cosx 15inS + 2inxS = 27cos + -1cosx 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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