How do you graph #r^2 = sin(2theta)#?

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Sep 11, 2016

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Explanation:

Try plotting with points.

Some easy points would be #(0,0)#, #(pi/12,+-1/sqrt2)#, #(pi/8,+-1/root(4)2)#, #(pi/6,+-root(4)3/sqrt2)#, #(pi/4,+-1)#, #((3pi)/8,+-1/root(4)2)#, #(pi/2,0)#.

From the equation, #sin(2theta)# cannot be negative, so #theta# is restricted to #0 <= theta<= pi/2# or #pi <= theta <= (3pi)/2#.

And most values of #theta# corresponds to a positive and a negative value of #r#, the graph should have rotational symmetry.

If a graphing program for cartesian is available, the cartesian equation is

#(x^2 + y^2)^2 = xy#

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