I don't understand what the distance is that they are asking

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I don't understand what this problem is asking for, any help would be appreciated:


"Consider the spiral r = θ and a ray—emanating from the pole—that intersects the spiral. What is the distance between any two consecutive points of intersection?
"










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  • $r=theta$ means that the point that is $r$ away from the origin makes an angle $theta$ in the plane.
    – Jason Kim
    Sep 1 at 3:20










  • I know the graph $r=theta$ but I don't understand what the distance is that they are asking
    – Pagaley 12
    Sep 1 at 3:22










  • @Pagaley12 I don't understand what the distance is that they are asking Does a ray from the origin intersect the spiral? Multiple times? Then the question is likely asking about the distance between two such consecutive intersections.
    – dxiv
    Sep 1 at 3:24











  • I think they were asking for me to draw a straight line from the origin at any angle and see the distance between two points that it intersects on the spiral
    – Pagaley 12
    Sep 1 at 3:25










  • @Pagaley12 Right. The spiral is $,r = theta,$, think at the equation of a ray now.
    – dxiv
    Sep 1 at 3:30














up vote
2
down vote

favorite












I don't understand what this problem is asking for, any help would be appreciated:


"Consider the spiral r = θ and a ray—emanating from the pole—that intersects the spiral. What is the distance between any two consecutive points of intersection?
"










share|cite|improve this question























  • $r=theta$ means that the point that is $r$ away from the origin makes an angle $theta$ in the plane.
    – Jason Kim
    Sep 1 at 3:20










  • I know the graph $r=theta$ but I don't understand what the distance is that they are asking
    – Pagaley 12
    Sep 1 at 3:22










  • @Pagaley12 I don't understand what the distance is that they are asking Does a ray from the origin intersect the spiral? Multiple times? Then the question is likely asking about the distance between two such consecutive intersections.
    – dxiv
    Sep 1 at 3:24











  • I think they were asking for me to draw a straight line from the origin at any angle and see the distance between two points that it intersects on the spiral
    – Pagaley 12
    Sep 1 at 3:25










  • @Pagaley12 Right. The spiral is $,r = theta,$, think at the equation of a ray now.
    – dxiv
    Sep 1 at 3:30












up vote
2
down vote

favorite









up vote
2
down vote

favorite











I don't understand what this problem is asking for, any help would be appreciated:


"Consider the spiral r = θ and a ray—emanating from the pole—that intersects the spiral. What is the distance between any two consecutive points of intersection?
"










share|cite|improve this question















I don't understand what this problem is asking for, any help would be appreciated:


"Consider the spiral r = θ and a ray—emanating from the pole—that intersects the spiral. What is the distance between any two consecutive points of intersection?
"







algebra-precalculus geometry polar-coordinates






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edited Sep 1 at 3:25

























asked Sep 1 at 3:14









Pagaley 12

225




225











  • $r=theta$ means that the point that is $r$ away from the origin makes an angle $theta$ in the plane.
    – Jason Kim
    Sep 1 at 3:20










  • I know the graph $r=theta$ but I don't understand what the distance is that they are asking
    – Pagaley 12
    Sep 1 at 3:22










  • @Pagaley12 I don't understand what the distance is that they are asking Does a ray from the origin intersect the spiral? Multiple times? Then the question is likely asking about the distance between two such consecutive intersections.
    – dxiv
    Sep 1 at 3:24











  • I think they were asking for me to draw a straight line from the origin at any angle and see the distance between two points that it intersects on the spiral
    – Pagaley 12
    Sep 1 at 3:25










  • @Pagaley12 Right. The spiral is $,r = theta,$, think at the equation of a ray now.
    – dxiv
    Sep 1 at 3:30
















  • $r=theta$ means that the point that is $r$ away from the origin makes an angle $theta$ in the plane.
    – Jason Kim
    Sep 1 at 3:20










  • I know the graph $r=theta$ but I don't understand what the distance is that they are asking
    – Pagaley 12
    Sep 1 at 3:22










  • @Pagaley12 I don't understand what the distance is that they are asking Does a ray from the origin intersect the spiral? Multiple times? Then the question is likely asking about the distance between two such consecutive intersections.
    – dxiv
    Sep 1 at 3:24











  • I think they were asking for me to draw a straight line from the origin at any angle and see the distance between two points that it intersects on the spiral
    – Pagaley 12
    Sep 1 at 3:25










  • @Pagaley12 Right. The spiral is $,r = theta,$, think at the equation of a ray now.
    – dxiv
    Sep 1 at 3:30















$r=theta$ means that the point that is $r$ away from the origin makes an angle $theta$ in the plane.
– Jason Kim
Sep 1 at 3:20




$r=theta$ means that the point that is $r$ away from the origin makes an angle $theta$ in the plane.
– Jason Kim
Sep 1 at 3:20












I know the graph $r=theta$ but I don't understand what the distance is that they are asking
– Pagaley 12
Sep 1 at 3:22




I know the graph $r=theta$ but I don't understand what the distance is that they are asking
– Pagaley 12
Sep 1 at 3:22












@Pagaley12 I don't understand what the distance is that they are asking Does a ray from the origin intersect the spiral? Multiple times? Then the question is likely asking about the distance between two such consecutive intersections.
– dxiv
Sep 1 at 3:24





@Pagaley12 I don't understand what the distance is that they are asking Does a ray from the origin intersect the spiral? Multiple times? Then the question is likely asking about the distance between two such consecutive intersections.
– dxiv
Sep 1 at 3:24













I think they were asking for me to draw a straight line from the origin at any angle and see the distance between two points that it intersects on the spiral
– Pagaley 12
Sep 1 at 3:25




I think they were asking for me to draw a straight line from the origin at any angle and see the distance between two points that it intersects on the spiral
– Pagaley 12
Sep 1 at 3:25












@Pagaley12 Right. The spiral is $,r = theta,$, think at the equation of a ray now.
– dxiv
Sep 1 at 3:30




@Pagaley12 Right. The spiral is $,r = theta,$, think at the equation of a ray now.
– dxiv
Sep 1 at 3:30










2 Answers
2






active

oldest

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up vote
0
down vote



accepted










It's not an answer but I think the problem is to find the Distance $AB$ in the figure. Choose the line (Red) suitably.








share|cite|improve this answer



























    up vote
    1
    down vote













    The spiral $r=theta$ looks like this:





    Note: Green is based off of $r$ is negative (which is seen as not counted).



    Since $theta$ repeats every $2pi,$ (well, it doesn't actually repeat, but $sin$ and $cos$ values are both the same value if $2pi$ gets added) the answer is $2pi.$






    share|cite|improve this answer






















    • Is $(0,0)$ a point of intersection? If not, why?
      – Ixion
      Sep 1 at 3:44










    • I don't quite understand this notation, so I can't explain.
      – Jason Kim
      Sep 1 at 3:46










    • Is the point of the plane $(0,0)$ (the origin) a point of intersection between the blue segment and the spiral? (Sorry, English is not my native language.)
      – Ixion
      Sep 1 at 3:48











    • :P I meant the problem notation
      – Jason Kim
      Sep 1 at 3:49










    • Ah, ok. :) The question is not precise enough. I mean, if $thetain [0,+infty)$ then one of two consecutive points must be $(0,0)$, hence the distance between them is $theta$ for all $thetain [0,2pi)$ (by definition). If $thetain (0,+infty)$ then your solution is perfect.
      – Ixion
      Sep 1 at 3:57










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    2 Answers
    2






    active

    oldest

    votes








    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    0
    down vote



    accepted










    It's not an answer but I think the problem is to find the Distance $AB$ in the figure. Choose the line (Red) suitably.








    share|cite|improve this answer
























      up vote
      0
      down vote



      accepted










      It's not an answer but I think the problem is to find the Distance $AB$ in the figure. Choose the line (Red) suitably.








      share|cite|improve this answer






















        up vote
        0
        down vote



        accepted







        up vote
        0
        down vote



        accepted






        It's not an answer but I think the problem is to find the Distance $AB$ in the figure. Choose the line (Red) suitably.








        share|cite|improve this answer












        It's not an answer but I think the problem is to find the Distance $AB$ in the figure. Choose the line (Red) suitably.









        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Sep 1 at 3:34









        Sujit Bhattacharyya

        496116




        496116




















            up vote
            1
            down vote













            The spiral $r=theta$ looks like this:





            Note: Green is based off of $r$ is negative (which is seen as not counted).



            Since $theta$ repeats every $2pi,$ (well, it doesn't actually repeat, but $sin$ and $cos$ values are both the same value if $2pi$ gets added) the answer is $2pi.$






            share|cite|improve this answer






















            • Is $(0,0)$ a point of intersection? If not, why?
              – Ixion
              Sep 1 at 3:44










            • I don't quite understand this notation, so I can't explain.
              – Jason Kim
              Sep 1 at 3:46










            • Is the point of the plane $(0,0)$ (the origin) a point of intersection between the blue segment and the spiral? (Sorry, English is not my native language.)
              – Ixion
              Sep 1 at 3:48











            • :P I meant the problem notation
              – Jason Kim
              Sep 1 at 3:49










            • Ah, ok. :) The question is not precise enough. I mean, if $thetain [0,+infty)$ then one of two consecutive points must be $(0,0)$, hence the distance between them is $theta$ for all $thetain [0,2pi)$ (by definition). If $thetain (0,+infty)$ then your solution is perfect.
              – Ixion
              Sep 1 at 3:57














            up vote
            1
            down vote













            The spiral $r=theta$ looks like this:





            Note: Green is based off of $r$ is negative (which is seen as not counted).



            Since $theta$ repeats every $2pi,$ (well, it doesn't actually repeat, but $sin$ and $cos$ values are both the same value if $2pi$ gets added) the answer is $2pi.$






            share|cite|improve this answer






















            • Is $(0,0)$ a point of intersection? If not, why?
              – Ixion
              Sep 1 at 3:44










            • I don't quite understand this notation, so I can't explain.
              – Jason Kim
              Sep 1 at 3:46










            • Is the point of the plane $(0,0)$ (the origin) a point of intersection between the blue segment and the spiral? (Sorry, English is not my native language.)
              – Ixion
              Sep 1 at 3:48











            • :P I meant the problem notation
              – Jason Kim
              Sep 1 at 3:49










            • Ah, ok. :) The question is not precise enough. I mean, if $thetain [0,+infty)$ then one of two consecutive points must be $(0,0)$, hence the distance between them is $theta$ for all $thetain [0,2pi)$ (by definition). If $thetain (0,+infty)$ then your solution is perfect.
              – Ixion
              Sep 1 at 3:57












            up vote
            1
            down vote










            up vote
            1
            down vote









            The spiral $r=theta$ looks like this:





            Note: Green is based off of $r$ is negative (which is seen as not counted).



            Since $theta$ repeats every $2pi,$ (well, it doesn't actually repeat, but $sin$ and $cos$ values are both the same value if $2pi$ gets added) the answer is $2pi.$






            share|cite|improve this answer














            The spiral $r=theta$ looks like this:





            Note: Green is based off of $r$ is negative (which is seen as not counted).



            Since $theta$ repeats every $2pi,$ (well, it doesn't actually repeat, but $sin$ and $cos$ values are both the same value if $2pi$ gets added) the answer is $2pi.$







            share|cite|improve this answer














            share|cite|improve this answer



            share|cite|improve this answer








            edited Sep 1 at 4:52

























            answered Sep 1 at 3:37









            Jason Kim

            53216




            53216











            • Is $(0,0)$ a point of intersection? If not, why?
              – Ixion
              Sep 1 at 3:44










            • I don't quite understand this notation, so I can't explain.
              – Jason Kim
              Sep 1 at 3:46










            • Is the point of the plane $(0,0)$ (the origin) a point of intersection between the blue segment and the spiral? (Sorry, English is not my native language.)
              – Ixion
              Sep 1 at 3:48











            • :P I meant the problem notation
              – Jason Kim
              Sep 1 at 3:49










            • Ah, ok. :) The question is not precise enough. I mean, if $thetain [0,+infty)$ then one of two consecutive points must be $(0,0)$, hence the distance between them is $theta$ for all $thetain [0,2pi)$ (by definition). If $thetain (0,+infty)$ then your solution is perfect.
              – Ixion
              Sep 1 at 3:57
















            • Is $(0,0)$ a point of intersection? If not, why?
              – Ixion
              Sep 1 at 3:44










            • I don't quite understand this notation, so I can't explain.
              – Jason Kim
              Sep 1 at 3:46










            • Is the point of the plane $(0,0)$ (the origin) a point of intersection between the blue segment and the spiral? (Sorry, English is not my native language.)
              – Ixion
              Sep 1 at 3:48











            • :P I meant the problem notation
              – Jason Kim
              Sep 1 at 3:49










            • Ah, ok. :) The question is not precise enough. I mean, if $thetain [0,+infty)$ then one of two consecutive points must be $(0,0)$, hence the distance between them is $theta$ for all $thetain [0,2pi)$ (by definition). If $thetain (0,+infty)$ then your solution is perfect.
              – Ixion
              Sep 1 at 3:57















            Is $(0,0)$ a point of intersection? If not, why?
            – Ixion
            Sep 1 at 3:44




            Is $(0,0)$ a point of intersection? If not, why?
            – Ixion
            Sep 1 at 3:44












            I don't quite understand this notation, so I can't explain.
            – Jason Kim
            Sep 1 at 3:46




            I don't quite understand this notation, so I can't explain.
            – Jason Kim
            Sep 1 at 3:46












            Is the point of the plane $(0,0)$ (the origin) a point of intersection between the blue segment and the spiral? (Sorry, English is not my native language.)
            – Ixion
            Sep 1 at 3:48





            Is the point of the plane $(0,0)$ (the origin) a point of intersection between the blue segment and the spiral? (Sorry, English is not my native language.)
            – Ixion
            Sep 1 at 3:48













            :P I meant the problem notation
            – Jason Kim
            Sep 1 at 3:49




            :P I meant the problem notation
            – Jason Kim
            Sep 1 at 3:49












            Ah, ok. :) The question is not precise enough. I mean, if $thetain [0,+infty)$ then one of two consecutive points must be $(0,0)$, hence the distance between them is $theta$ for all $thetain [0,2pi)$ (by definition). If $thetain (0,+infty)$ then your solution is perfect.
            – Ixion
            Sep 1 at 3:57




            Ah, ok. :) The question is not precise enough. I mean, if $thetain [0,+infty)$ then one of two consecutive points must be $(0,0)$, hence the distance between them is $theta$ for all $thetain [0,2pi)$ (by definition). If $thetain (0,+infty)$ then your solution is perfect.
            – Ixion
            Sep 1 at 3:57

















             

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