rock.freak667 said:If you had y=cosθ, cosθ is dimensionless but θ would be in radians. What should x be then?
JustSomeGuy80 said:an angle? arc length?
An equation is dimensionally correct if the units on each side of the equation are the same. This means that the units for each variable in the equation must match on both the left and right sides. For example, if the left side of the equation has units of meters per second, the right side must also have units of meters per second for the equation to be dimensionally correct.
Dimensional correctness is important because it ensures that the units of measurement in the equation are consistent and accurate. If an equation is not dimensionally correct, it could lead to incorrect results and can also indicate errors in the equation itself.
No, an equation must not only have matching units on each side, but it must also make sense in terms of the physical quantities being represented. For example, an equation that calculates the volume of a cube cannot have units of meters per second, as volume is not a measure of speed.
To check if an equation is dimensionally correct, you can break down each variable and its corresponding unit and see if they match on both sides of the equation. You can also use dimensional analysis, which involves converting all units to their base units and cancelling out any units that appear on both sides of the equation.
Some common mistakes include forgetting to convert units, using incorrect units, or not including all variables and their corresponding units in the equation. It is also important to check for consistency in units, such as using either all metric or all imperial units in the equation.