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convert equation 8x=8y to polar form

Elissa89

Member
Oct 19, 2017
52
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
 

topsquark

Well-known member
MHB Math Helper
Aug 30, 2012
1,121
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
 

Elissa89

Member
Oct 19, 2017
52
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)
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,736
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 \(\theta\)?
 

Elissa89

Member
Oct 19, 2017
52
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.
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,736
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:

\(\displaystyle \tan(\theta)=1\) ?
 

Elissa89

Member
Oct 19, 2017
52
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
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,736

Elissa89

Member
Oct 19, 2017
52

MarkFL

Administrator
Staff member
Feb 24, 2012
13,736
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.
 

Elissa89

Member
Oct 19, 2017
52
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