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

In summary, the Cartesian equation $y=\sin(x)$ can be written in polar form as $r=1$ and the implicit polar equation $r\sin(\theta)=\sin(r\cos(\theta))$ can be used to plot the equation. This is equivalent to a circle of radius 1 centered at the origin.
  • #1
karush
Gold Member
MHB
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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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  • #2
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?
 
  • #3
so it's not a sinx wave
 
  • #4
The Cartesian version of the polar equation $r=1$ is:

\(\displaystyle x^2+y^2=1\)

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

The Cartesian equation:

\(\displaystyle y=\sin(x)\)

will have the implicit polar relation:

\(\displaystyle r\sin(\theta)=\sin(r\cos(\theta))\)
 
  • #5
apreciate the added help
the book was short on explaining things
my major source of learning is MHB
 

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

What is the polar form of $\sin x$?

The polar form of $\sin x$ is $r\sin\theta$, where $r$ is the length of the vector from the origin to the point on the unit circle and $\theta$ is the angle formed by the vector and the positive x-axis.

How do you convert a simple equation into polar form?

To convert a simple equation into polar form, you can use the substitution $x=r\cos\theta$ and $y=r\sin\theta$. Then, solve for $r$ and $\theta$ by using trigonometric identities and algebraic manipulation.

What are the common mistakes when solving for the polar form of $\sin x$?

Some common mistakes when solving for the polar form of $\sin x$ include forgetting to use the substitution $x=r\cos\theta$ and $y=r\sin\theta$, not using the correct trigonometric identities, and making errors in algebraic manipulation.

Can you provide an example of solving for the polar form of $\sin x$?

Yes, an example of solving for the polar form of $\sin x$ is converting the simple equation $x^2+y^2=1$ into polar form. Using the substitution $x=r\cos\theta$ and $y=r\sin\theta$, we get $r^2(\cos^2\theta+\sin^2\theta)=1$. Simplifying this equation yields $r=1$, which is the polar form of $\sin x$.

Why is it important to know how to solve for the polar form of $\sin x$?

Knowing how to solve for the polar form of $\sin x$ allows you to represent complex equations in a simpler form, making them easier to manipulate and solve. This can be particularly useful in fields such as physics and engineering, where polar coordinates are often used to describe the position and movement of objects.

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