Havent found anyone who can answer will mark brainliest in the essay box below, write a pair of parametric equations for an object moving along the unit circle. (hint: how is a point on the unit circle defined? ) on a separate sheet of graph paper, graph the curve that is traced by a point for the following parametric equations as the parameter varies over the domain 0 ≤ t ≤ 2 π : x = 2cost y = 2sint create a table of values like the one shown above (you may need to upload your table from a word processing program). show at least five points. on a separate sheet of graph paper, graph the curve that is traced by a point for the following parametric equations as the parameter varies over the domain 0 ≤ t ≤ 2 π : x = 4cost y = 2sint create a table of values like the one shown above (you may need to upload your table from a word processing program). show at least five points. based on your work above, write any inferences you have about parametric equations of the form x = acost and y = bsint, for a = b and a ≠ b.

Look at the unit circle and apply the hint. The x- and y-coordinates of each point are cosθ and sinθ, respectively. The radius of the unit circle is, of course, 1, and the center point is (0, 0).

General form of the parametric equations for a circle:

x = r·cosθ+h

and

y = r·sinθ+k

where r is the radius and (h, k) is the center. Therefore, the parametric equations for the unit circle are

x = cosθ

and

y = sinθ

The parametric equations

x = 2cosθ

and

y = 2sinθ

define a circle of radius 2, centered at the origin.

The parametric equations

x = 4cosθ

and

y = 2sinθ

define a horizontal ellipse centered at the origin, with transverse axis of length 8 and conjugate axis of length 4.

If a = b then

x = a·cosθ

and

y = b·sinθ

define a circle centered at the origin.

If a > b, then

x = a·cosθ

and

y = b·sinθ

define a horizontal ellipse centered at the origin.

If a < b, If a = b then

x = a·cosθ

and y = b·sinθ

define a vertical ellipse centered at the origin.

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283 square feet

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