How to graph r 2 = cos ( 2 θ ) ?

Question

How to graph             r      2        =          cos              (        2        θ        )            ?

Zachariah Patel · Accepted Answer

the first and fourth quadrants             |      θ      |        ≤          π      4       In the 2nd and 3rd,             |      π      -      θ      |        ≤          π      4      .  I used infinity symbol       ∞   to depict the shape of this double-loop, looking like a fallen 8. For getting 8-erect, the equation is             r      2        =    -          cos      2        θ  Use a table             {              (        r        ,        θ        )            }        .    =          {              (        0        ,        -                  π          4                )                    (                  1                      2                          ,        -                  π          8                )                    (        1        ,        0        )                    (                  1                      2                          ,                  π          8                )                    (        0        ,                         π      4        )    }  , for one loop. Its mirror image with respect to       θ    =          π      2       is the other loop.Strictly,         r    =                            x          2                +                  y          2                      ≥    0  . Graphs of both             r      2        =    ±          cos      2        θ   are combined.

How to graph r^2=cos(2theta)?

Answered question

Answer & Explanation

New Questions in Integral Calculus