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Simplifying 3cos(2X) + -2sin(2x) = (a) * sin(bx + c) Remove parenthesis around (2X) 3cos * 2X + -2sin(2x) = (a) * sin(bx + c) Reorder the terms for easier multiplication: 3 * 2cos * X + -2sin(2x) = (a) * sin(bx + c) Multiply 3 * 2 6cos * X + -2sin(2x) = (a) * sin(bx + c) Multiply cos * X 6cosX + -2sin(2x) = (a) * sin(bx + c) Remove parenthesis around (2x) 6cosX + -2ins * 2x = (a) * sin(bx + c) Reorder the terms for easier multiplication: 6cosX + -2 * 2ins * x = (a) * sin(bx + c) Multiply -2 * 2 6cosX + -4ins * x = (a) * sin(bx + c) Multiply ins * x 6cosX + -4insx = (a) * sin(bx + c) Multiply a * ins 6cosX + -4insx = ains(bx + c) 6cosX + -4insx = (bx * ains + c * ains) 6cosX + -4insx = (abinsx + acins) Solving 6cosX + -4insx = abinsx + acins Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-1acins' to each side of the equation. 6cosX + -1acins + -4insx = abinsx + acins + -1acins Reorder the terms: -1acins + 6cosX + -4insx = abinsx + acins + -1acins Combine like terms: acins + -1acins = 0 -1acins + 6cosX + -4insx = abinsx + 0 -1acins + 6cosX + -4insx = abinsx Add '4insx' to each side of the equation. -1acins + 6cosX + -4insx + 4insx = abinsx + 4insx Combine like terms: -4insx + 4insx = 0 -1acins + 6cosX + 0 = abinsx + 4insx -1acins + 6cosX = abinsx + 4insx Reorder the terms: -1abinsx + -1acins + 6cosX + -4insx = abinsx + 4insx + -1abinsx + -4insx Reorder the terms: -1abinsx + -1acins + 6cosX + -4insx = abinsx + -1abinsx + 4insx + -4insx Combine like terms: abinsx + -1abinsx = 0 -1abinsx + -1acins + 6cosX + -4insx = 0 + 4insx + -4insx -1abinsx + -1acins + 6cosX + -4insx = 4insx + -4insx Combine like terms: 4insx + -4insx = 0 -1abinsx + -1acins + 6cosX + -4insx = 0 Factor out the Greatest Common Factor (GCF), 's'. s(-1abinx + -1acin + 6coX + -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 '(-1abinx + -1acin + 6coX + -4inx)' equal to zero and attempt to solve: Simplifying -1abinx + -1acin + 6coX + -4inx = 0 Solving -1abinx + -1acin + 6coX + -4inx = 0 Move all terms containing c to the left, all other terms to the right. Add 'abinx' to each side of the equation. -1abinx + -1acin + 6coX + abinx + -4inx = 0 + abinx Reorder the terms: -1abinx + abinx + -1acin + 6coX + -4inx = 0 + abinx Combine like terms: -1abinx + abinx = 0 0 + -1acin + 6coX + -4inx = 0 + abinx -1acin + 6coX + -4inx = 0 + abinx Remove the zero: -1acin + 6coX + -4inx = abinx Add '4inx' to each side of the equation. -1acin + 6coX + -4inx + 4inx = abinx + 4inx Combine like terms: -4inx + 4inx = 0 -1acin + 6coX + 0 = abinx + 4inx -1acin + 6coX = abinx + 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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