How do you convert #x^2-y^2=1 # to polar form?

1 Answer
Jim G.
Jul 17, 2016

#r^2=sec2theta#

Explanation:

To convert from #color(blue)"cartesian to polar" # use the following.

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

We will also make use of the identities.

#color(orange)"Reminder"#

#color(red)(|bar(ul(color(white)(a/a)color(black)(cos2theta=cos^2theta-sin^2theta)color(white)(a/a)|)))#

and #color(red)(|bar(ul(color(white)(a/a)color(black)(sectheta=1/(costheta))color(white)(a/a)|)))#

Using the conversion formulae above we can write.

#x^2-y^2=1rArr(rcostheta)^2-(rsintheta)^2=1#

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

#rArrr^2(cos^2theta-sin^2theta)=1rArrr^2=1/(cos^2theta-sin^2theta)#

#rArrr^2=1/(cos2theta)=sec2theta#

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