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

slaggingV 2021-08-20 Answered
Give two pairs of parametric equations that generate a circle centered at the origin with radius 6.

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tabuordg
Answered 2021-08-21 Author has 7361 answers
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.
\(\displaystyle{x}^{{2}}+{y}^{{2}}={6}^{{2}}\)
\(\displaystyle{x}^{{2}}+{y}^{{2}}={36}\)
Now, using formula here as \(\displaystyle{{\sin}^{{2}}\theta}+{{\cos}^{{2}}\theta}={1}\),
Using the above formula to create the parametric equation which are given as,
\(\displaystyle{x}{\left({t}\right)}={6}{\sin{{t}}}\)
and \(\displaystyle{y}{\left({t}\right)}={\cos{{t}}}\) where t in \(\displaystyle{\left[{0},{2}\pi\right]}\)
Simlarily, we can formulate the second parametric equation as,
\(\displaystyle{x}{\left({t}\right)}={6}{\cos{{t}}}\)
and \(\displaystyle{y}{\left({t}\right)}={\sin{{t}}}\) where t in \(\displaystyle{\left[{0},{2}\pi\right]}\)
Answer: The pair of parametric equations of a circle centered at origin and the radius is 6  are \(\displaystyle{x}{\left({t}\right)}={6}{\sin{{t}}}\) and \(\displaystyle{y}{\left({t}\right)}={\cos{{t}}}\)
where t in \(\displaystyle{\left[{0},{2}\pi\right]}\) and \(\displaystyle{x}{\left({t}\right)}={6}{\cos{{t}}}\)
and \(\displaystyle{y}{\left({t}\right)}={\sin{{t}}}\) where t in \(\displaystyle{\left[{0},{2}\pi\right]}\)
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