Constrain Conical Helix to an Included Angle

Hi, first post and 30+ years since my last math class.

I am trying to construct a tapered helix that is constrained to a specific included angle. I have the equations for a tapered helix given height, pitch, radii, but cannot get my head around how to force the helix to grow within a given included angle.

X(t) = ( R1 + (t*(R2-R1) / (2*T*PI)) )*COS(t)

Y(t) = q*( R1 + (t*(R2-R1)) / (2*T*PI) )*SIN(t)

Z(t) = (H*t)/(2*T*PI)

where

R1 = big radius

R2 = small radius

T = number of turns (f(pitch,height))

H = height

q = handedness

Google tells me a lot about antennae and DNA, but not much about this. Any help appreciated.

wf