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Simplifying x(t) = cos(6280t) * cos(628t) + -0.5cos(3.14 * 1800t) Multiply x * t tx = cos(6280t) * cos(628t) + -0.5cos(3.14 * 1800t) Remove parenthesis around (6280t) tx = cos * 6280t * cos(628t) + -0.5cos(3.14 * 1800t) Remove parenthesis around (628t) tx = cos * 6280t * cos * 628t + -0.5cos(3.14 * 1800t) Reorder the terms for easier multiplication: tx = 6280 * 628cos * t * cos * t + -0.5cos(3.14 * 1800t) Multiply 6280 * 628 tx = 3943840cos * t * cos * t + -0.5cos(3.14 * 1800t) Multiply cos * t tx = 3943840cost * cos * t + -0.5cos(3.14 * 1800t) Multiply cost * cos tx = 3943840c2o2s2t * t + -0.5cos(3.14 * 1800t) Multiply c2o2s2t * t tx = 3943840c2o2s2t2 + -0.5cos(3.14 * 1800t) Multiply 3.14 * 1800 tx = 3943840c2o2s2t2 + -0.5cos(5652t) Remove parenthesis around (5652t) tx = 3943840c2o2s2t2 + -0.5cos * 5652t Reorder the terms for easier multiplication: tx = 3943840c2o2s2t2 + -0.5 * 5652cos * t Multiply -0.5 * 5652 tx = 3943840c2o2s2t2 + -2826cos * t Multiply cos * t tx = 3943840c2o2s2t2 + -2826cost Reorder the terms: tx = -2826cost + 3943840c2o2s2t2 Solving tx = -2826cost + 3943840c2o2s2t2 Solving for variable 't'. Reorder the terms: 2826cost + -3943840c2o2s2t2 + tx = -2826cost + 3943840c2o2s2t2 + 2826cost + -3943840c2o2s2t2 Reorder the terms: 2826cost + -3943840c2o2s2t2 + tx = -2826cost + 2826cost + 3943840c2o2s2t2 + -3943840c2o2s2t2 Combine like terms: -2826cost + 2826cost = 0 2826cost + -3943840c2o2s2t2 + tx = 0 + 3943840c2o2s2t2 + -3943840c2o2s2t2 2826cost + -3943840c2o2s2t2 + tx = 3943840c2o2s2t2 + -3943840c2o2s2t2 Combine like terms: 3943840c2o2s2t2 + -3943840c2o2s2t2 = 0 2826cost + -3943840c2o2s2t2 + tx = 0 Factor out the Greatest Common Factor (GCF), 't'. t(2826cos + -3943840c2o2s2t + x) = 0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(2826cos + -3943840c2o2s2t + x)' equal to zero and attempt to solve: Simplifying 2826cos + -3943840c2o2s2t + x = 0 Solving 2826cos + -3943840c2o2s2t + x = 0 Move all terms containing t to the left, all other terms to the right. Add '-2826cos' to each side of the equation. 2826cos + -3943840c2o2s2t + -2826cos + x = 0 + -2826cos Reorder the terms: 2826cos + -2826cos + -3943840c2o2s2t + x = 0 + -2826cos Combine like terms: 2826cos + -2826cos = 0 0 + -3943840c2o2s2t + x = 0 + -2826cos -3943840c2o2s2t + x = 0 + -2826cos Remove the zero: -3943840c2o2s2t + x = -2826cos Add '-1x' to each side of the equation. -3943840c2o2s2t + x + -1x = -2826cos + -1x Combine like terms: x + -1x = 0 -3943840c2o2s2t + 0 = -2826cos + -1x -3943840c2o2s2t = -2826cos + -1x Divide each side by '-3943840c2o2s2'. t = 0.0007165605096c-1o-1s-1 + 0.0000002535599821c-2o-2s-2x Simplifying t = 0.0007165605096c-1o-1s-1 + 0.0000002535599821c-2o-2s-2x Reorder the terms: t = 0.0000002535599821c-2o-2s-2x + 0.0007165605096c-1o-1s-1Solution
t = {0, 0.0000002535599821c-2o-2s-2x + 0.0007165605096c-1o-1s-1}
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