If you say you need a 45 degree taper - is that the inclusive angle, in other words if the piece was purely turned down to a point on the end and you held a square against the point it would only fill up half of the square ? - from your drawing it appears that is what you want.
If so, you need to set your top slide to half of the angle offset to turn it (22.5 degrees). Setting your top slide at 45 degrees will give a 90 degree inclusive angle.
From your comment that your top slide is set normally to 29.5 degrees for thread cutting, it appears that your top slide scale is marked to read 0 when the top slide travel is parallel to your cross slide travel and thus square to the stock in the lathe... If this is the case, you'll actually have to set the top slide to
a) 67.5 degrees with your top slide handle to the left front of the lathe.
or
b) 112.5 degrees with the top slide handle to the right rear of the lathe.
The main disadvantage with a) is that you could end up twiddling the cross slide dial very close to the chuck - watch the clearance carefully, and be safe; it's a prime position to lose a finger. The advantage is you can use tailstock support.
For b), it's a lot safer to turn, but you cannot use tailstock support.
2 cents...
, Arnold
