Let C be the curve parametrized by $$x=3sint,\;y=4t,\;z=3cost,\;t\geq 0$$ a)if you start at the point (0,0,3) and move $5\pi$ units along C, you end up at a point $(z,y,z)=(a,b,c)$. Find the coordinates of a,b and c.

b)Find the curvatuce of C at the point (a,b,c) found in a

Question

Let C be the curve parametrized by $$x=3sint,\;y=4t,\;z=3cost,\;t\geq 0$$ a)if you start at the point (0,0,3) and move $5\pi$  units along C, you end up at a point $(z,y,z)=(a,b,c)$. Find the coordinates of a,b and c.

b)Find the curvatuce of C at the point (a,b,c) found in a

anonymous · Answer

Hi,
a) since starting point is (0,0,3) this means t=0. Therefore t of the ending point is 0+5pi = 5pi. Now insert t=5pi into the coordinates. This yields x=a=3sin5pi = 3sin pi = 0, y=b=4*5pi = 20pi, z = 3cos5pi = 3cospi = -3