MHB Solving Polar Form of $\sin x$: Simple Equations

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The discussion revolves around converting the equation \( y = \sin(x) \) into polar form, which simplifies to \( r = 1 \). However, this leads to confusion as \( r = 1 \) represents a circle rather than a sine wave. The Cartesian equivalent of the polar equation \( r = 1 \) is \( x^2 + y^2 = 1 \), indicating both represent circles of radius 1 centered at the origin. The implicit polar relation for the Cartesian equation is given by \( r\sin(\theta) = \sin(r\cos(\theta)) \). The participants express a need for clearer explanations, highlighting the shortcomings of their learning resources.
karush
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$$y=\sin\left({x}\right) $$
write in polar form

This reduces to $$r=1$$

So that's not = plots

Not sure why I can't get these simple equations
 
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karush said:
$$y=\sin\left({x}\right) $$
write in polar form

This reduces to $$r=1$$

So that's not = plots

Not sure why I can't get these simple equations

Why do you think r = 1 is wrong?
 
so it's not a sinx wave
 
The Cartesian version of the polar equation $r=1$ is:

$$x^2+y^2=1$$

Both are circles of radius 1, centered at the origin.

The Cartesian equation:

$$y=\sin(x)$$

will have the implicit polar relation:

$$r\sin(\theta)=\sin(r\cos(\theta))$$
 
apreciate the added help
the book was short on explaining things
my major source of learning is MHB
 
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