r(t)=6sin(2t)+6cos(2t)+5t

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Solution for r(t)=6sin(2t)+6cos(2t)+5t equation:


Simplifying
r(t) = 6sin(2t) + 6cos(2t) + 5t

Multiply r * t
rt = 6sin(2t) + 6cos(2t) + 5t

Remove parenthesis around (2t)
rt = 6ins * 2t + 6cos(2t) + 5t

Reorder the terms for easier multiplication:
rt = 6 * 2ins * t + 6cos(2t) + 5t

Multiply 6 * 2
rt = 12ins * t + 6cos(2t) + 5t

Multiply ins * t
rt = 12inst + 6cos(2t) + 5t

Remove parenthesis around (2t)
rt = 12inst + 6cos * 2t + 5t

Reorder the terms for easier multiplication:
rt = 12inst + 6 * 2cos * t + 5t

Multiply 6 * 2
rt = 12inst + 12cos * t + 5t

Multiply cos * t
rt = 12inst + 12cost + 5t

Reorder the terms:
rt = 12cost + 12inst + 5t

Solving
rt = 12cost + 12inst + 5t

Solving for variable 'r'.

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

Divide each side by 't'.
r = 12cos + 12ins + 5

Simplifying
r = 12cos + 12ins + 5

Reorder the terms:
r = 5 + 12cos + 12ins

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