Question

Graph each polar equation. Also, identify the type of polar graph.r = 2 + 2 cos θ

Accepted Answer

Recognize that the given polar equation is of the form $$r = a + b \cos 	heta$$, which typically represents a limaçon curve. The values of $$a$$ and $$b$$ will determine the specific shape (cardioid, dimpled limaçon, or limaçon with an inner loop). Identify the constants: here, $$a = 2$$ and $$b = 2. $$Since $$a = b$$, this suggests the graph is a cardioid, a special type of limaçon. To graph the equation, create a table of values by choosing several values of $$	heta ($$for example, $$0$$, $$\frac{\pi}{6}$$, $$\frac{\pi}{4}$$, $$\frac{\pi}{2}$$, $$\pi$$, etc.) and calculate the corresponding $$r$$ values using $$r = 2 + 2 \cos 	heta. $$Plot the points $$(r, 	heta) on $$polar coordinates, where $$r is $$the radius (distance from the origin) and $$	heta is $$the angle measured from the positive x-axis. Connect these points smoothly to reveal the shape of the graph. Confirm the shape by noting that when $$	heta = 0$$, $$r is $$maximum ($$r = 4$$), and when $$	heta = \pi$$, $$r is $$minimum ($$r = 0$$), which matches the behavior of a cardioid.

Graph each polar equation. Also, identify the type of polar graph.
r = 2 + 2 cos θ

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Polar Coordinates and Equations

Types of Polar Graphs

Graphing Polar Equations