trigonometric graphs transformations

if you have a graph of something like tan(theta +45) , I know that you have to move the graph to the left 45 degrees, but if you think about it, you're getting a larger angle right, so surely it should be a transformation to the RIGHT of 45 degrees if that makes sense. Please could someone explain this? ty xx

You have a variable translation
z = x + 45
or
x = z - 45
You're plotting tan() in the original space x, so for the translated tan(), the origin z=0 shifts to x=-45. The translated graph is 45 to the left of the original one.

The way I think about it is the graphs have x on the x-axis not the angle. In tan(x+45) x is smaller than the x in tan(x) at a given position on the tan curve.

Not sure if I make any sense but I hope this helps