How do you graph $r^{2} = sin (2 θ)$ $r^2 = sin(2theta)$ ?

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How do you graph $r^{2} = sin (2 θ)$ $r^2 = sin(2theta)$ ?

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Answer 1 · 2016-09-11T13:00:08

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Explanation:

Try plotting with points.

Some easy points would be $(0, 0)$ $(0,0)$ , $(\frac{π}{12}, \pm \frac{1}{\sqrt{2}})$ $(pi/12,+-1/sqrt2)$ , $(\frac{π}{8}, \pm \frac{1}{\sqrt[4]{2}})$ $(pi/8,+-1/root(4)2)$ , $(\frac{π}{6}, \pm \frac{\sqrt[4]{3}}{\sqrt{2}})$ $(pi/6,+-root(4)3/sqrt2)$ , $(\frac{π}{4}, \pm 1)$ $(pi/4,+-1)$ , $(\frac{3 π}{8}, \pm \frac{1}{\sqrt[4]{2}})$ $((3pi)/8,+-1/root(4)2)$ , $(\frac{π}{2}, 0)$ $(pi/2,0)$ .

From the equation, $sin (2 θ)$ $sin(2theta)$ cannot be negative, so $θ$ $theta$ is restricted to $0 \leq θ \leq \frac{π}{2}$ $0 <= theta<= pi/2$ or $π \leq θ \leq \frac{3 π}{2}$ $pi <= theta <= (3pi)/2$ .

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

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

${(x^{2} + y^{2})}^{2} = x y$ $(x^2 + y^2)^2 = xy$

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How do you graph $r^{2} = sin (2 θ)$ $r^2 = sin(2theta)$ ?

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How do you graph $r^{2} = sin (2 θ)$ $r^2 = sin(2theta)$ ?