Is the following dimensional equation dimensionally consiste

Is the following dimensional equation dimensionally consistent? Explain. ML = ML cos(L_t).

Solution

The value inside the cosine must be nondimensional and is usually expressed in radians. Therefore, the result of your cosine is also dimensionless. Lets say Lt = 1 radian, therefore cos(1) = 0.540 (unitless!).

You should also be careful in using cos(Lt)=Lt because this case is only true in a small angle approximation; at larger angles, this assumption becomes inaccurate fast.