I am running into an issue when I am trying to do this parametric equation problem. I tried solving it multiple ways but I think I keep doing it wrong somehow as I get different answers. The ones I have below are the latest. How would I approach this problem as each time I do it I get different answers.
Current Answers (Only x is right): x(t)=1-3t y(t)=3t z(t)=1+2t
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.
x = e^(-3t)cos(4t)
y = e^(-3t)sin(4t)
z=e^(-3t)
Point: (1,0,1)
What is x(t), y(t), and z(t)? x(t) is 1-3t as that is the only correct part
To solve this I took the derivative with respect to t for each point, then plugged in t=0 to solve for the directional vector. Once I did that I just plugged in the points with that vector to get the parametric equations.
x(t) = 1-3t
y(t) = 4t
z(t) = 1-3t