Give two pairs of parametric equations that generate a circle centered at the origin with radius 6.

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tabuordg · Accepted Answer

Given: A circle centered at the origin and radius 6.  To find: the two pairs of parametric equations   Concept used: in polar coordinates a point in the plane is identified by a pair of numbers(r, theta), where r and theta both are coordinate of the parametric system   Explanation: Let there is  a point (x,y)which belong to the circle which centered at origin and have radius of 6 unit.     x2+y2=62     x2+y2=36  Now, using formula here as sin2θ+cos2θ=1,  Using the above formula to create the parametric equation which are given as,       x(t)=6sin⁡t   and y(t)=cos⁡t where t in [0,2π]  Simlarily, we can formulate the second parametric equation as,          x(t)=6cos⁡t   and y(t)=sin⁡t where t in [0,2π]  Answer: The pair of parametric equations of a circle centered at origin and the radius is 6  are  x(t)=6sin⁡t and y(t)=cos⁡t   where t in [0,2π] and  x(t)=6cos⁡t   and y(t)=sin⁡t where t in [0,2π]

Give two pairs of parametric equations that generate a circle centered at the origin with

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