Convert equation 8x=8y to polar form

In summary: Yeah I shot him a message, I just hope he gets back to me in time, assignment is due tonight at midnight.
  • #1
Elissa89
52
0
Convert the equation to polar form

8x=8y

I thought it would be

8*r*cos(theta)=8*r*sin(theta)

Said it was incorrect

then I thought I needed to divide by 8 to remove it, giving me:

r*cos(theta)=r*sin(theta)

But that was also incorrect and now I am stuck
 
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  • #2
Elissa89 said:
Convert the equation to polar form

8x=8y

I thought it would be

8*r*cos(theta)=8*r*sin(theta)

Said it was incorrect

then I thought I needed to divide by 8 to remove it, giving me:

r*cos(theta)=r*sin(theta)

But that was also incorrect and now I am stuck
Either there's a typo somewhere or this is too simple a problem.

Your difficulty is that you stopped too soon. You can also divide by r (assuming that it's not zero). Thus you have the equation: \(\displaystyle cos( \theta ) = sin( \theta )\). There are several possible values for \(\displaystyle \theta\).

-Dan
 
  • #3
topsquark said:
Either there's a typo somewhere or this is too simple a problem.

Your difficulty is that you stopped too soon. You can also divide by r (assuming that it's not zero). Thus you have the equation: \(\displaystyle cos( \theta ) = sin( \theta )\). There are several possible values for \(\displaystyle \theta\).

-Dan
Nope, no typo. I also tried cos(theta)=sin(theta). Then I thought I need to get the r alone and I got r=r*tan(theta)
 
  • #4
Elissa89 said:
Nope, no typo. I also tried cos(theta)=sin(theta). Then I thought I need to get the r alone and I got r=r*tan(theta)

If you divided through by \(r\), you have:

\(\displaystyle \tan(\theta)=1\)

What does this imply for \(\theta\)?
 
  • #5
MarkFL said:
If you divided through by \(r\), you have:

\(\displaystyle \tan(\theta)=1\)

What does this imply for \(\theta\)?

I tried inputting pi/4 and 5pi/4, but it doesn't want an answer, it wants the question converted to a polar equation.
 
  • #6
Elissa89 said:
I tried inputting pi/4 and 5pi/4, but it doesn't want an answer, it wants the question converted to a polar equation.

Any Cartesian line of the form:

\(\displaystyle y=ax\)

will correspond to a polar equation of the form:

\(\displaystyle \tan(\theta)=a\)

or:

\(\displaystyle \theta=\arctan(a)+k\pi\)

Only a line not passing through the origin will have a polar equation involving both \(r\) and \(\theta\).

Did you try inputting:

\(\displaystyle \tan(\theta)=1\) ?
 
  • #7
MarkFL said:
Any Cartesian line of the form:

\(\displaystyle y=ax\)

will correspond to a polar equation of the form:

\(\displaystyle \tan(\theta)=a\)

or:

\(\displaystyle \theta=\arctan(a)+k\pi\)

Only a line not passing through the origin will have a polar equation involving both \(r\) and \(\theta\).

Did you try inputting:

\(\displaystyle \tan(\theta)=1\) ?

Yes, it didn't take it
 
  • #8
Elissa89 said:
Yes, it didn't take it

Perhaps it wants:

\(\displaystyle \theta=\frac{\pi}{4}(4k+1)\)
 
  • #9
MarkFL said:
Perhaps it wants:

\(\displaystyle \theta=\frac{\pi}{4}(4k+1)\)

It still didn't take it
 
  • #10
Elissa89 said:
It still didn't take it

At this point, I would recommend you speak to the professor, and let him/her know what you've done.
 
  • #11
MarkFL said:
At this point, I would recommend you speak to the professor, and let him/her know what you've done.

Yeah I shot him a message, I just hope he gets back to me in time, assignment is due tonight at midnight
 

FAQ: Convert equation 8x=8y to polar form

1. How do you convert a linear equation to polar form?

To convert a linear equation in the form of y = mx + b to polar form, we first need to substitute r for y and θ for x. This is because in polar coordinates, r represents the distance from the origin and θ represents the angle from the positive x-axis. So, the equation becomes r = mθ + b.

2. What is the formula for converting a linear equation to polar form?

The formula for converting a linear equation in the form of y = mx + b to polar form is r = mθ + b. This formula is derived from the fact that in polar coordinates, the point (r,θ) can be represented as (r cosθ, r sinθ), where r is the distance from the origin and θ is the angle from the positive x-axis.

3. Is there a specific range for θ when converting to polar form?

Yes, there is a specific range for θ when converting to polar form. In general, θ should be between 0 and 2π radians, or 0 and 360 degrees. This ensures that all possible values of θ are included in the conversion.

4. Can any linear equation be converted to polar form?

No, not every linear equation can be converted to polar form. This conversion is only applicable to equations that have a linear relationship between x and y. Equations that have higher degree terms, such as quadratic or cubic equations, cannot be converted to polar form.

5. How does converting an equation to polar form change its graph?

Converting an equation from rectangular form to polar form changes the graph from a line or curve on a Cartesian plane to a spiral or circle on a polar plane. This is because the variables have been changed from x and y to r and θ, which represent distance and angle, respectively. The shape of the graph will depend on the specific equation and its parameters.

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