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raddian
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Homework Statement
For the following dimensional equation, find the base dimensions of the parameter f:
M M-3 = a cos( f L )
Homework Equations
M represents mass, a represents acceleration due to gravity, in terms of mass * length over seconds squared [[M * L]/[t2]] where L represents length and t represents time.
For example, solving for k in the equation:
ML2 = k L t M2
results in k = L M-1 t-1
The Attempt at a Solution
The answer, which is given, is L-1,
So I got
cos-1(M-2 a-1) = f L
the output of the cos-1 function results in a dimensionless unit of measure (radian/degree).
Therefore,
c = f L
where c is a constant/dimensionless quantity,
therefore f = L -1
The problem is that I cannot understand how the inverse cosine function works in this sense. Can its input be "dimensionally inequivalent", I can't find the word for it.
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