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Numerade Educator

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Problem 10 Medium Difficulty

Sketch the curve with the given vector equation. Indicate with an arrow the direction in which $ t $ increases.

$ r(t) = \langle \sin \pi t , t , \cos \pi t \rangle $

Answer

see work for graph

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Video Transcript

So what we're given is that our our position um, position vector is sign piety T Kherson Patty. So we know that the why values going to constantly increase, um and then the x n Z values are going to make a circular pattern, so it's gonna end up giving us a spiral shape, and it's going to look like this. So since this is our why right here, we wanted to be going in this direction. So we're going to end up having is something that looks like this continues on and on. We can use an increment of pi over six. Um, and if we just create a table of values, we can graph that. We see that the spiral goes and the positive y axis direction. So we see that it will go like this and then like this, like this so we can draw those arrows just to give in a sense of which direction it's moving. Um, and that's because we know that X equals co sign T and y equals Sign T gives us a circle. So if we have signed pity coastline, pity that's going to give us a circle and the tea is the Y values, so that's gonna just constantly increase as T increases