Question

here's the question: solve for cos(2theta)=1

if you graph r= cos(2Theta)

then graph r=1

you find that there are four places where the graphs intersect.

however, when solved algebraically, there are two solutions which can be represented in an infinitely many format as: Theta = pi(K) (where k= an integer.)

so why do the graphs imply the answer should be Theta = pi(k)/2 ? What am I missing?

Answer 1

cos(2Ø) = 1
2Ø = 0 or 2Ø = 2π
Ø = 0 or Ø = π


Now here is the problem:
Are you graphing on a rectangular graph where Ø is the horizontal axis and r is the vertical axis
OR
Are you graphing in polar coordinates ???

I will illustrate:
let y = cos(2x), and y = 1

http://www.wolframalpha.com/input/?i=plot+y+%3D+cos%282x%29%2C+y+%3D+1+for+0+%3C+x+%3C+2%CF%80

notice the multiples of π intersections ---> kπ

now in polar:

http://www.wolframalpha.com/input/?i=plot+r+%3D+cos%282%C3%98%29%2C+r+%3D+1+

Don't know why the graphs are separate, let's blame Wolfram, but you can see they would intersect in 4 places


Does that shed some light on the situation?