Recent content by vcsharp2003

Is n a unit vector? And do x and x0 also denote vectors? My guess is that n can denote a normal unit vector or a normal non-unit vector, but it must be normal to the straight line whose equation is being sought. And x denotes the position vector of any variable point on the straight line whose...

Thank you for helping me solve this problem..

It seems complex, but I will try. So, I am going to restrict to the interval ##\omega \in [0,2\pi)## since all other values of ##\omega## will simply be a repeat of the corresponding value in this interval. One thing that comes to my mind is that the edge cases would be ##x = \pm {5}## and...

So, I must deal with the special cases ##\sin{\omega} =0## and ##\cos{\omega} =0## in my proposed solution.

I am trying to understand the variable ##\omega##, since the one-liner solution makes no mention of it. It seems that this variable is the angle from the positive x-axis to the radius in an anti-clockwise direction, as shown in the diagram below. If that's correct, then the solution should be...

I get that since a tangent to a circle will always be perpendicular to its radius. But, the question still remains how the one-liner solution was arrived at and what does ##\omega## variable in the solution represent? Maybe it involves a long derivation.

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given...

It seems that none of the options given in the challenge problem under post#13 is true. I counted the number of intersections in post#10 to be greater than 16. I also counted the number of intersections as 2 in post#3 . In that case, shouldn't this challenge problem be wrong?

Its a Math book titled Mathematics 11 that is used in Grade 11 in schools of Ontario, Canada. The publisher is McGraw-Hill Ryerson and it has multiple authors from various school boards of Ontario, Canada. You can see a full legal copy of it at the Internet Archive using the following link...

Thank you so much for this example. It helped greatly in understanding the problem. It seems that the number of intersections has no upper limit.

Sorry, you're correct. I didn't paste the original question at the start. The exact problem as it appears in the Math book is as below. From what I have gathered so far from all the replies is that the answer to this exact question is none of the given options since as the curvature of the...

Yes, the problem seems accurate. It's a challenge problem in a high school text book.

Please give me the clue as I have tried your suggestion, but still I can't see the logic.

If it's a straight line there would be many peaks of the sin wave that it would touch. If we take it further down so it is on the x-axis then also there would be many points on the sine curve that it would intersect.

I tried your recommendation on the desmos.com graphing calculator and I was always getting 2 points of intersection for various circles that I tried. Below are three scenarios that I tried, and they all always intersect at two points. But logically, I cannot arrive at this conclusion of two...