F(t)=18cos(t)+9sin(2t)

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Solution for F(t)=18cos(t)+9sin(2t) equation: 


Simplifying
F(t) = 18cos(t) + 9sin(2t)

Multiply F * t
tF = 18cos(t) + 9sin(2t)

Multiply cos * t
tF = 18cost + 9sin(2t)

Remove parenthesis around (2t)
tF = 18cost + 9ins * 2t

Reorder the terms for easier multiplication:
tF = 18cost + 9 * 2ins * t

Multiply 9 * 2
tF = 18cost + 18ins * t

Multiply ins * t
tF = 18cost + 18inst

Solving
tF = 18cost + 18inst

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-18cost' to each side of the equation.
-18cost + tF = 18cost + -18cost + 18inst

Combine like terms: 18cost + -18cost = 0
-18cost + tF = 0 + 18inst
-18cost + tF = 18inst

Add '-18inst' to each side of the equation.
-18cost + -18inst + tF = 18inst + -18inst

Combine like terms: 18inst + -18inst = 0
-18cost + -18inst + tF = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(-18cos + -18ins + F) = 0


Subproblem 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 = 0

Subproblem 2
Set the factor '(-18cos + -18ins + F)' equal to zero and attempt to solve:

Simplifying
-18cos + -18ins + F = 0

Reorder the terms:
F + -18cos + -18ins = 0

Solving
F + -18cos + -18ins = 0

Move all terms containing t to the left, all other terms to the right.

Add '-1F' to each side of the equation.
F + -18cos + -1F + -18ins = 0 + -1F

Reorder the terms:
F + -1F + -18cos + -18ins = 0 + -1F

Combine like terms: F + -1F = 0
0 + -18cos + -18ins = 0 + -1F
-18cos + -18ins = 0 + -1F
Remove the zero:
-18cos + -18ins = -1F

Add '18cos' to each side of the equation.
-18cos + 18cos + -18ins = -1F + 18cos

Combine like terms: -18cos + 18cos = 0
0 + -18ins = -1F + 18cos
-18ins = -1F + 18cos

Add '18ins' to each side of the equation.
-18ins + 18ins = -1F + 18cos + 18ins

Combine like terms: -18ins + 18ins = 0
0 = -1F + 18cos + 18ins

Simplifying
0 = -1F + 18cos + 18ins

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
t = {0}

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