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Match the vector equations in Exercises $1 - 8$ with the graphs $( a ) - ( h )$ given here.

$$

\mathbf { r } ( t ) = ( 2 \cos t ) \mathbf { i } + ( 2 \sin t ) \mathbf { j } , \quad 0 \leq t \leq 2 \pi

$$

graph g

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okay. Were given a vector equation R of T is equal to to co sign of tea. Um, I plus two sign of T j, um, and T goes from zero to two pi inclusive, and we want to match it up to one of the grafts that ours on. Um, Paige Nice. 9 60 in your book. Um, and so that, um, graph is gonna be graft G. And let's talk about why, um so I is in the X Jay is in the UAE, and so we have nothing and nothing at all in the sea. And so that means that thes to have to be in on the X y playing. And of course, we should recognize that, um, co sign t plus a sign t in a vector or Parametric situation is going to be a circle with a radius with a radius of two. And of course, is gonna go. It's gonna be a full circle because time or T goes from 0 to 2 pi. So if I look at all of my choices, the only one and let me try to draw him. So here's my Z axis. Um and of course, my why And then, Of course, my ex is the one that is coming out of the board. And so, um, if I look at the graph, this is going to be, um, a circle with a radius of two just in the, um quips that should go the other way just in the x y plane. And so that's why I know it is, um, Option G. Because now the other options give me that circle and I should start rate recognizing this is a parametric equation. And so this would be to co sign t you put the two sign t is is gonna be a circle.

University of Central Arkansas