Question

Determine the type of symmetry of r =5-sin11ø from the equation, if any. Make sure to confirm graphically. Symmetric with respect to the:

A) pole
B) line /2
C) polar axis
D) none of these

Answer 1

well, let me not bore you to death on how we test it and test it.

`\underline{\textit{testing for symmetry to the }(\pi )/(2)~line\qquad \qquad r=-r~~,~~\theta =-\theta } \\\\\\ r=5-sin(11\theta )\implies (-r)=5-sin[11(-\theta )]\implies -r=5-sin(-11\theta ) \\\\\\ \stackrel{symmetry~identity}{-r=5-\stackrel{\downarrow }{[-sin(11\theta )]}}\implies\implies r=-5-sin(11\theta )\impliedby \textit{no dice} \\\\[-0.35em] ~\dotfill`

`\underline{\textit{testing for symmetry to the polar axis}\qquad \qquad \theta =-\theta} \\\\\\ r=5-sin(11\theta )\implies r=5-sin[11(-\theta )]\implies r=5-sin(-11\theta ) \\\\\\ r=5-[-sin(11\theta )]\implies r=5+sin(11\theta )\impliedby \textit{no dice} \\\\[-0.35em] ~\dotfill`

`\underline{\textit{testing for symmetry to the pole}\qquad \qquad r=-r} \\\\\\ r=5-sin(11\theta )\implies -r=5-sin(11\theta )\implies r=-5+sin(11\theta )\qquad \textit{no dice}`

so the symmetry tests didn't pass, notice the picture below though, looks a bit deceiving, it looks as if it'd have π/2 symmery, but it doesn't show in the test.