Answer:
(Sin(5)+5Cos(5), Cos(5)-5Sin(5), 9)
Step-by-step explanation:
The equation of tangent line is [tex]r(t)+t*r^{'}(t)[/tex], then:
[tex]r(t)=(Sin(5t), Cos(5t), 2^{\frac{7}{2} } )[/tex] and [tex]r^{'} (t)=(5Cos(5t), -5Sin(5t), 7t^{\frac{5}{2} })[/tex], we have to (x,y,z) coordinates
x=r(t)+tr'(t), y=r(t)+tr'(t), z=r(t)+tr'(t); so x=Sin(5t)+t(5Cos(5t)), y=Cos(5t)+t(-5Sin(5t)), [tex]z=2t^{\frac{7}{2} }+7t^{\frac{5}{2} }[/tex], to t=1 then:
x=Sin(5)+5Cos(5), y=Cos(5)-5Sin(5), Z=9; Finally (Sin(5)+5Cos(5), Cos(5)-5Sin(5), 9)
