## Polar coordinate System and converting equations from polar to rectangular and viceversa

Polar coordinate system is a plane with Pole(point O) and polar axis  which is horizontal axis from point O. Any point P in this plane is assigned polar coordinates represented as P(r, theta)

we measure theta as positive when moving counterclockwise and negative when moving clockwise.

If r > 0, then P is on the terminal side of  theta . If r < 0, then P is on the terminal side of   (theta + pi).
{"ft_lang_label":"__label__en","ft_lang_prob":0.83866215,"math_prob":0.99124515,"size":785,"snap":"2023-40-2023-50","text_gpt3_token_len":201,"char_repetition_ratio":0.11011524,"word_repetition_ratio":0.27450982,"special_character_ratio":0.27388534,"punctuation_ratio":0.11258278,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9871121,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-10-02T09:00:18Z\",\"WARC-Record-ID\":\"<urn:uuid:66278f7f-0c21-46a6-bd6c-90cf4b194321>\",\"Content-Length\":\"68716\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:786afed5-c85a-4452-a12f-be6a55e192a6>\",\"WARC-Concurrent-To\":\"<urn:uuid:dd0ad3c1-b2cb-405f-864f-8d11ce39cac4>\",\"WARC-IP-Address\":\"34.237.19.89\",\"WARC-Target-URI\":\"https://celestialtutors.com/2019/06/\",\"WARC-Payload-Digest\":\"sha1:XDKDXQLYRY4YY2FIXIFLIOYHYNNPMZK2\",\"WARC-Block-Digest\":\"sha1:J5HMVJS7VCOFT443XSGCSIEZTD6GIKOZ\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-40/CC-MAIN-2023-40_segments_1695233510983.45_warc_CC-MAIN-20231002064957-20231002094957-00635.warc.gz\"}"}