Polar Graph Exploration

Expresión 13: "r" equals "a" plus "b" cosine theta

Expresión 14: "b" equals 0.2

Changing b results in a reflection over the y-axis. Changing a results in a larger graph with a longer radius all around. The sine of the graph is shifted because of the differing starting points and outputs of sine at the same values.

The Third

Expresión 17: "r" equals "a" StartRoot, cos theta , EndRoot

Changing a reflects the graph over the y-axis. It also affects the radius and size of the graph, higher a values enlarge the graph. The sine of the graph is shifted because of the differing starting points and outputs of sine at the same values.

The Fourth

Expresión 20: "r" equals "a" plus "b" theta

Enlarging a results in a smaller graph, while shrinking a results in a larger, more scattered arrangement. It affects the radius and the center as well. The variable, b, affects how many curves are present in the cardioid(s) at the center.

The Fifth

Expresión 23: "r" equals "a" "e" Superscript, "k" theta , Baseline

Expresión 24: "k" equals 7.7

The variable, k, affects the magnitude and size of the graph. As k grows, the graph becomes much wider and more expansive. Variable a affects the starting point of the graph on the x-axis. However, when the a slider is brought on the negative side of zero, the line flips along the line y=x. With a at zero, the line is not existent because zero times the rest of the equation yields zero.

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