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Currently I'm trying to figure out an equation for a graph on any angle (say a sin curve). The reason for this is to make the "flight paths" of the ships in the game more interesting. Right now they basically fly towards a target from any angle.

So far, I've figured out that for a normal sin curve along the x-axis, the equation is (0 degrees):

x = t

y = sin(t)

And along the y-axis is (90 degrees):

x = sin(t)

y = t

Now what I'm trying to figure out is how to make the sin graph appear on any angle, say along a 45 degree angle.

Can anyone help me figure out an equation for that? I know this is probably simple, but I'm only a first year engineering student and haven't spent much time on parametric curves :p.

Thanks!