‘... it wouldn't let me.’
Of course it will!
You just have to ask it nicely (and ask the correct plotting function)!
syms t
x(t) = (sqrt(3)*t- sin(t))/2
y(t) = (t + sqrt(3)*sin(t))/2
z(t) = 0*t
figure
fplot3(x, y, z, [-1 1]*25, 'LineWidth',2)
Make appropriate changes to get the desired result.
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