Question #5b70d

2 Answers
Eddie
Mar 7, 2017

#r = pm 1#

Explanation:

This is the unit circle about the Origin

  • Take the parameterisation in polar coordinates:

#x = r cos theta, y = r sin theta#

  • Observe that:

#x^2 + y^2 = r^2(cos^2 theta + sin^2 theta) = r^2#,

  • Then note that you actually have:

#r^2 = 1, r = pm 1#

I'd go with the #pm # bit too. I've seen it argued that #r# should only ever be positive, though I can't remember the detail and it makes no sense to me (albeit I say that as a user of maths as opposed to mathematician).

.

Jim G.
Mar 7, 2017

#r^2=1#

Explanation:

To convert from #color(blue)"cartesian to polar form"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(x=rcostheta;y=rsintheta)color(white)(2/2)|)))#

#x^2+y^2=1#

#rArr(rcostheta)^2+(rsintheta)^2=1#

#rArrr^2cos^2theta+r^2sin^2theta=1#

#rArrr^2(cos^2theta+sin^2theta)=1#

#rArrr^2=1" since "cos^2theta+sin^2theta=1#

This is the equation of a circle, centred at the origin with radius 1

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