1Thanks
• 1 Post By eddie2042

# Thread:

1. ## Finding Period of polar graph

How come the polar graph of $r=a cos\Theta$ or $r=a sin\Theta$ only has a period of a pi?
To find the period I would use $\frac{2\pi}{b}$, so why wouldnt the period of both these polar circles be $2\pi$

2. ## Re: Finding Period of polar graph

Originally Posted by delgeezee
How come the polar graph of $r=a cos\Theta$ or $r=a sin\Theta$ only has a period of a pi?
To find the period I would use $\frac{2\pi}{b}$, so why wouldnt the period of both these polar circles be $2\pi$
Consider $r = a\cos(\theta)$, which is a circle of radius a/2, centered at a/2. From 0 to pi/2 , $\cos(\theta)$ is positive, so r is positive. From pi/2 to pi, $\cos(\theta)$ is negative, which makes r negative as well. On a graph, a negative r implies that the line starts from the origin and proceeds in the direction opposite to that which the corresponding angle points to.

So at theta=0, r = a, and theta=pi, r = -a, which are the same point.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9421395659446716, "perplexity_flag": "middle"}