Why is there never a tan2?

Question

The function atan2 accepts 2 variables x and y so it can return an angle of a range of 2pi instead of pi. But why is there never tan2 which is then the exact opposite of atan2 and returns 2 values x and y based on the given angle? Is there a simpler method to get the directional vector of an angle I'm missing?

Answer 1

The deep reason is probably because FORTRAN functions return a single value.

Indeed, y= sin(x), x= cos(x) is what you need. (Alternatively, y= r * sin(x), x= r * cos(x) allows you to provide a vector length.)

This lack is a frustration for both users and implementors, because it is quite frequent to need both values at the same time, while this would allow optimizing away some common computations.

Answer 2

Well tan2 dosent exist because there isnt a single value of x and y that satisfies tan (theta) since tan is the ratio of opposite by adjacent.

Let us say that tan2 did exist Then tan2 (60°) would return

opp=sqrt (3)    &    adj=1

Since tan(60°)= opp/adj = sqrt (3)

But it could also return

opp=3           &    adj=sqrt (3)

And that would also be equal to sqrt (3);

Since tan is a ratio it returns only one value , that is The ratio of opposide to adjacent

And also in most programming languages a function can return only one value