Do functions have units?

So, in conclusion, either is fine as long as what actually defines your function is consistent with dimensions/units. The only important thing is that physical equation must contain terms whose physical dimensions are homogeneous.

Can an exponential function have units?

From that follows, that the argument of the exponential must not carry a unit, because the exponential is defined as a power series. ex=∞∑n=0xnn! If x were to carry a unit, say meters, one would add (schematically) m+m2+m3+⋯, which is nonsenical.

Why are trigonometric ratios dimensionless?

Trigonometric ratios are dimensionless because the numerator and denominator have the same dimension, if they have one at all.

Do trigonometric functions have units?

Trigonometric functions don’t “preserve” units. The expression under a trigonometric function must be dimensionless and so is the value of a trigonometric function.

Does cosine have a unit?

Does a transfer function have units?

The unit of τ is sec. Assuming again that the unit of s is rad/sec, a/(s+a) is not without a unit.

What is the unit of exponent?

Simply defined, an exponent is a shorthand notation for the number of times a number is multiplied by itself. For example, n to the fourth power is shorthand for n times n times n times n, or n times itself four times. N to the second power, or n squared, is equal to n times n, or n times itself twice.

Does sine have a unit?

Since the result of sin(2) does not have any units attached to it, it is impossible from the outset to use the units of the result to interpret the same sine operation to give the right result no matter whether we meant 2 degrees or 2 radians.

What is the unit and dimension of impulse?

In classical mechanics, impulse (symbolized by J or Imp) is the integral of a force, F, over the time interval, t, for which it acts. The SI unit of impulse is the newton second (N⋅s), and the dimensionally equivalent unit of momentum is the kilogram meter per second (kg⋅m/s).

Why is the unit circle important?

The Unit Circle: A Basic Introduction The unit circle, or trig circle as it’s also known, is useful to know because it lets us easily calculate the cosine, sine, and tangent of any angle between 0° and 360° (or 0 and 2π radians).

Does the argument of the exponential function carry a unit?

Obviously you cannot add, e.g meters and seconds, but multiplying to form m / s as a unit for velocity is a valid operation. From that follows, that the argument of the exponential must not carry a unit, because the exponential is defined as a power series. e x = ∑ n = 0 ∞ x n n!

Why is time a non-real function?

The reason is quite boringly that these functions are only defined for real numbers, or perhaps integers, complex numbers, real vectors. But time is none of these. The only exception you can make are homogeneous functions, especially linear functions.

Why are there no units for the dimensions in physics?

“Dimensions”, in the sense that you are using the word (meters, kilograms, degrees Celcius) are not mathematical objects, they are physical. If you are asking why no physics formula, with exponents, has no units on the exponent, you will have to ask a physicist.

Is the argument of Sine dimensionless or dimensionless?

The argument of sine (ie k t) should be dimensionless – eg an angle in degrees or a fraction of 2 π. However if k is dimensionless and t is time then k t has units of time and is not dimensionless. So this combination of units cannot be correct. Highly active question.