Polar Graphs

r = a cos $\theta$ §

as the value of a gets bigger the diameter / radius of the circle also gets bigger

diameter = value of a

if a > 0 The circle is to the right of the origin else if a < 0 The circle is to the left of the origin

r = a sin $\theta$ §

as the value of a gets bigger the diameter / radius also gets bigger

diameter = value of a

if a > 0 The circle is above the origin else if a < 0 The circle is below the origin

r = a cos n$\theta$ §

These graphs are called Rose Curves If the value of n is an even number then number of “loops” is 2n (Eg: if n is 2 then the number of loops is 4)

If the value of n is an odd number then the number of “loops” is n (Eg: if n is 3 then the number of loops is 3)

The diameter of each loop = a (doesn’t matter even or odd)

If n = 1 then it’s a normal circle graph

r = a sin n$\theta$ §

These graphs are called Rose Curves If the value of n is an even number then number of “loops” is 2n (Eg: if n is 2 then the number of loops is 4)

If the value of n is an odd number then the number of “loops” is n (Eg: if n is 3 then the number of loops is 3)

The diameter of each loop = a (doesn’t matter even or odd)

If n = 1 then it’s a normal circle graph

r = a + b sin $\theta$ §

These graphs are also called limaçons

if a > b then the graph makes a weird shape, not exactly a circle

if b > a then the graph makes a weird inner loop, (amongus character?)

r = a - b sin $\theta$ §

These graphs are also called limaçons if a > b then the weird line goes on the top

if a < b then the loop in the other figure goes on the top

r = a + b cos $\theta$ §

These graphs are also called limaçons if a > b then the weird line goes on the left

if a < b then the weird loop goes on the left

r = a - b cos $\theta$ §

These graphs are also called limaçons if a > b then the weird line goes on the right

if a < b then the weird loop goes on the right

r = a + a sin $\theta$ §

Graphs are called cardiods if a > 0 then we get this shape that’s upwards

if a < 0 then we get this shape that’s downwards

r = a - a sin $\theta$ §

Graphs are called cardiods if a > 0 then the graph looks like this

r = a + a cos $\theta$ §

Graphs are called cardiods if a > 0 the graphs look like this

r = a - a cos $\theta$ §

Graphs are called cardiods if a > 0 the graphs look like this

r = $\sqrt{a^{2}cos(2\theta )}$ §

These graphs are called lemniscates Graphs look like this for any a value (since it’s a${}^2$)

r = $\sqrt{a^{2}sin(2\theta )}$ §

These graphs are called lemniscates Graphs look like this for any a value (since it’s a${}^2$)