How do you graph $r = 4 cos θ + 4$ $r=4costheta+4$ ?

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Answer 1 · 2016-09-30T09:33:35

For details, see explanation.

$r = a (1 + cos (θ - α))$ $r=a(1+cos (theta-alpha))$ represents a family of cardioids,

emanating from the pole r =0.

Name reminds you of Heart symbol.

a and $α$ $alpha$ are parameters

$θ = α$ $theta = alpha$ is the line of symmetry..

a gives the size of a member of this family..

Maximum r =2a, at (2a, $α$ $alpha$ ).

Here, in r = 4 ( 1 + cos $θ$ $theta$ ), a = 4 and $α$ $alpha$ =0.

A short Table for graphing is given below.

$(r, θ) : (0, 8) (2 \sqrt{2}, \frac{π}{4}), (2, \frac{π}{2}) (0, π)$ $(r, theta): (0, 8) (2sqrt 2, pi/4), (2, pi/2) (0, pi)$ , for upper half.that

comprises a larger part in $Q_{1}$ $Q_1$ and a smaller in $Q_{2}$ $Q_2$ .

Use symmetry about $θ = 0$ $theta = 0$ , for the lower half.

How do you graph r=4cosθ+4r=4costheta+4?