In trigonometry, why is theta used in periodic function equations instead of x?

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Could it be that ∅ is used specifically for angles whereas x is used for an unknown quantity in general ?

x may relate to length. Theta is angle and it has no dimension. For sin and cosine values one needs the dimensionless values. Therefore. for the space variable you have kx (dimension less) and wt ( dimension less). Therefore theta, the angle is used.

There is NO reason to use θ instead of x; it's simply a question of convention. Mathematicians like to use greek letters to denote angles; x is usually used to denote a variable. So long as your notation is consistent and doesn't cause confusion throughout your work, there is no problem using x instead of θ.

The Greek letter θ (theta) is often used for an angle in mathematics.

For regular algebraic functions, y and x are used as the variables and usually represent real numbers. Now, in trig, the horizontal axis is still real numbers, but special reals that represent angles, and if you are graphing using radians then you no longer number the horizontal axis as 1, 2, 3 etc but are now numbered as multiples of pi. This reinforces that we are dealing with angles.

Because theta is specifically for angles

Because x has been used to death.

Greek letters are often used when representing *angles*, Θ (theta) is one example of that.

I was wondering why pi is used to represent the ratio of a circle's circumference to its diameter. I was thinking rho would be a better symbol.