Question

Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases. r(t)=cos(t)I -cos(t)j+sin(t)k
I don't know what to do. I let x=cos(t), y=-cos(t) and z= sin(t). Should I let t be any number and get the equal values for cosine and sine and start ploting or there something else to do?

Answer 1

They said sketch it. Start at t = 0, do t in degrees so you can see change easily
t |x y z
0| 1 , -1 , 0
1| .99 ,-.99, .02
9| .99,-.99,.15
20|.94,-.94, .34 note z changing faster than others
now look at change of r with change in t
dr/dt = -sin t i + sin t j + cos t k
at t = 0
dr/dt = 0 i + 0 j + 1 k
so at t = 0, r is headed up totally in z