# convert equation 8x=8y to polar form

#### Elissa89

##### Member
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
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
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

Staff member
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
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

Staff member
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
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

Staff member
Yes, it didn't take it
Perhaps it wants:

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

#### Elissa89

##### Member
Perhaps it wants:

$$\displaystyle \theta=\frac{\pi}{4}(4k+1)$$
It still didn't take it