aflacatn

2021-08-16

Is it true that the equations r=8, ${x}^{2}+{y}^{2}=64$ , and $x=8\mathrm{sin}\left(3t\right),y=8\mathrm{cos}\left(3t\right)(0\le t\le 2\pi )$ all have the same graph.

Aubree Mcintyre

Skilled2021-08-17Added 73 answers

2.Now, we will check that what type of equation is the r=8

This equation is the polar form equation in which we consider

So,

Thus, we can say that after changing polar co-ordinates to Cartesian co-ordinates, equation r=8 is also the equation of the circle with radius a=8 and center at (0,0).

So, the graphs of the equation

r=8 and

Now, we have the parametric form equations given as:

and

as by trigonometry identity

thus, we have shown that these parametric equations from circle with radius 8 and center at (0,0).

So, these parametric equations

4. So, the given statement is true as the equation

r=8 ,

origin.Thus, all these equations have the same graph given above.

Answer: it`s TRUE

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