The arguments of any of the standard mathematical functions such as trigonometric functions (such as sine and cosine), logarithms, or exponential functions that appear in the equation must be dimensionless. These functions require pure numbers as inputs and give pure numbers as outputs.

Is trigonometric functions a dimensionless quantity?

The proof that this gives you the familiar trigonometric sine if x is the ratio of two carefully chosen lengths takes you through a surprisingly interesting swath of mathematics. The quantity kt is dimensionless.

Is the sine function dimensionless?

Some quantities have no dimensions. For example, the sine of an angle is defined as the ratio of the lengths of two particular sides of a triangle. Thus, the dimensions of the sine are L/L, or 1. Therefore, the sine function is said to be "dimensionless".