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## Homework Statement

Find the unit tangent vector T(t) and find a set of parametric equations for the line tangent to the space curve at point P

r(t)= <2sin(t), 2cos(t), 4sin

^{2}(t)>, P(1, √3, 1)

## The Attempt at a Solution

I found T(t) using the formula T(t)= r'(t)/||r'(t)||

r'(t)= <2cos(t), -2sin(t), 8sin(t)cos(t)>

∴ T(t)= <2cos(t), -2sin(t), 8sin(t)cos(t)>/ 2+8sin(t)cos(t)

-note: i could do more to the denominator as far as trig functions and algebra but i dont know if it is useful.

What i don't understand is how the point is used to find the parametric equation.