At what points does the helix intersect the sphere ?

MATHEMATICS · Subjective · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

At what points does the helix r(t)=⟨sin⁡t,cos⁡t,t⟩\mathbf{r}(t) = \langle \sin t, \cos t, t \rangle intersect the sphere x2+y2+z2=5x^2 + y^2 + z^2 = 5 ?

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