[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-572173-105":53,"doc-detail-572173-en":120},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":113,"head_meta":115,"extra_data":117,"updated_unix":119},105,"en","unit-circle-cheat-sheet-trigonometric-values-and-methods","Unit Circle Cheat Sheet - Trigonometric Values and Methods","","A practical guide for using the unit circle to obtain trigonometric function values for any angle, explaining how to read cosine and sine coordinates and how to move anti-clockwise for positive angles and clockwise for negative angles. It covers finding values beyond 360° and includes shortcuts for larger angles using SOHCAHTOA, quadrant sign rules, and memorization methods. Summary tables and patterns for 30°, 45°, 60°, 90°, and multiples support fast recall, plus an approach for multiples of 90° via plotting key points.",{"@graph":63,"@context":112},[64,80,95],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":36,"@type":70,"position":76},"https://docshare.wps.com/template/forms/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/unit-circle-cheat-sheet-trigonometric-values-and-methods/572173/",4,{"url":78,"name":59,"@type":81,"author":82,"headline":59,"publisher":85,"fileFormat":88,"inLanguage":57,"description":61,"dateModified":89,"datePublished":89,"encodingFormat":88,"isAccessibleForFree":90,"interactionStatistic":91},"DigitalDocument",{"name":83,"@type":84},"Levi","Person",{"url":68,"name":86,"@type":87},"DocShare","Organization","application/pdf","2026-10-13",true,{"@type":92,"interactionType":93,"userInteractionCount":4},"InteractionCounter",{"@type":94},"ViewAction",{"@type":96,"mainEntity":97},"FAQPage",[98,104,108],{"name":99,"@type":100,"acceptedAnswer":101},"How do you read sine and cosine values from the unit circle?","Question",{"text":102,"@type":103},"Locate 0° as the starting point, then use the coordinates at each angle: the D coordinate gives cosine and the E coordinate gives sine. Move anti-clockwise to get values for angles from 0° to 360°.","Answer",{"name":105,"@type":100,"acceptedAnswer":106},"What is the rule for negative angles and angles larger than 360°?",{"text":107,"@type":103},"Use clockwise motion to obtain trigonometric values for negative angles (e.g., −30° matches 330° anti-clockwise). For angles greater than 360°, keep going around the circle (e.g., 390°, 405°, 420°) to find the corresponding values.",{"name":109,"@type":100,"acceptedAnswer":110},"How can you find trig values for larger angles without recalculating everything?",{"text":111,"@type":103},"Memorize values for key acute angles (30°, 45°, 60°, 90°) and then use SOHCAHTOA plus quadrant sign rules. For example, knowing 45° lets you determine values for 135°, 225°, and 315° by adjusting signs based on the quadrant.","https://schema.org",{"og:url":78,"og:type":114,"og:title":59,"og:site_name":86,"og:description":61},"article",{"robots":116,"canonical":78},"index,follow",{"doc_id":118,"site_id":56},572173,1791925922,{"code":4,"msg":5,"data":121},{"doc_id":118,"user_id":122,"nickname":83,"user_avatar":123,"doc_module":9,"category_id":35,"category_name":36,"doc_title":59,"doc_description":61,"doc_content":124,"file_id":125,"file_url":126,"file_type":127,"file_size":128,"view_count":4,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":73,"language":129,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":130,"faqs":131,"seo_title":132,"seo_description":61,"update_tm":119,"read_time":9},7971461740909,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","© mymathscloud  \nHow do we use the unit circle?  \nLocate the start place at 0° . This is our starting point.  \nThe coordinates indicated at each of the angles give us the value of the trig functions (cos and sin) for that particular angle. The angles have been given in degrees and radians (the corresponding radian measures are right above the ° measures and have just been included for completenessmost courses will use degrees to introduce this topic so you can ignore these parts at first) .  \nThe D coordinate gives us the value of cos and the E coordinate gives us the value of sin for each angle shown. We go round in an anti-clockwise direction to get the values of sin and cos for angles from 0° to 360° as shown.  \nNote:  \n• We can also go around the unit circle in a clockwise direction will find the trig values for negative angles such as −30, −60, −90° etc. −30° clockwise will give the same value as 330° anti-clockwise.  \n• We can also go around the unit circle again to find the trig values for angles bigger than 360° such as  \n390°, 405°, 420°, 450° etc.  \nSummary Table Of Values For The Unit Circle Above  \n\n| Multiples of 30° and 45°: !\"°,%&°, +\"° etc |  |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  | !\"° | $%° | &\"° | 120° | 135° | 150° | 210° | 225° | 240° | 300° | 315° | 330° |\n| '() +(\" coordinate) | !\" | √\"\u003Cbr>\" | √$\u003Cbr>\" | √$\u003Cbr>\" | √\"\u003Cbr>\" | !\" | !\u003Cbr>−\u003Cbr>\" | √\"\u003Cbr>−\u003Cbr>\" | √$\u003Cbr>−\u003Cbr>\" | √$\u003Cbr>−\u003Cbr>\" | √\"\u003Cbr>−\u003Cbr>\" | !\u003Cbr>−\u003Cbr>\" |\n| ,-' +($ coordinate) | √$\u003Cbr>\" | √\"\u003Cbr>\" | !\" | !\u003Cbr>−\u003Cbr>\" | √\"\u003Cbr>−\u003Cbr>\" | √$\u003Cbr>−\u003Cbr>\" | √$\u003Cbr>−\u003Cbr>\" | √\"\u003Cbr>−\u003Cbr>\" | !\u003Cbr>−\u003Cbr>\" | !\" | √\"\u003Cbr>\" | √$\u003Cbr>\" |\n| ./) +\u003Cbr>!= \\#($%)\\#~~ ~~'' * | !√$\u003Cbr>| ! | √$ | −√$ | −! |  ! \u003Cbr>−\u003Cbr>√$ | !√$\u003Cbr>| 1 | √$ | −√$ | −! |  ! \u003Cbr>−\u003Cbr>√$ |\n\nAlternative method for finding angles of !\"°,%&° ()* +\"° ,-. : Use SOHCAHTOA  \nKey: Use SOHCAHTOA to find the values for the  \nangles ()°, *+°,,)°'() + = +)*,** , cos + = +-,./* , tan + = )-**/  \nAlternative Method For Larger Angles (over /\"°)  \nFrom knowing the values of the trig functions for the acute angles above (30°, 45° and 60°), we can find the values of the trig functions for larger angles. First, recall the signs of the trig functions in each quadrant shown on the right. Also recall that going anti-clockwise gives us positive anglesand clockwise gives us negative angles.  \nFor example, if we know the trig values for 45°, we can also work out the trig values for 135°, 225° and 315° .  \n| AB°\u003Cbr>We know these values since we are meant to memorise the values of trig functions for angles 30, 45° , 60° and 90° . We draw an angle of 45° .\u003Cbr>|  | 5CB°\u003Cbr>We draw an angle of 135° which leaves an angle of 45° in the 2nd quadrant. We know that the trig values will be the exact same as for 45°, we just have the worry about the signs in the 2nd quadrant.\u003Cbr>|\n| --- | --- | --- |\n| ??B°\u003Cbr>We draw an angle of 135° which leaves an angle of 45° in the 3rd quadrant. We know that the trig values will be the exact same as for 45°, we just have the worry about the signs in the 3rd quadrant. |  | C5B°\u003Cbr>We draw an angle of 315° which leaves an angle of 45° in the 4th quadrant. We know the trig values will be the same as for 45°, we just have the worry about the signs in the 4th quadrant. |\n| tan is positive, but sin and cos\u003Cbr>are negative in quadrant 3 | | cos is positive, but sin and tan\u003Cbr>are negative in quadrant 4\u003Cbr>|\n\n| Multiples of /\"°: /\"°, 01\"°, 23\"°, !+\"° etc |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- |\n| | \"° |  | 0\"° | 12\"° | 34\"° | !&\"° |\n| \u003Cbr>567 +(\" coordinate) | ' |  | ! | ' | −! | \u003Cbr>' |\n| \u003Cbr>,-' +($ coordinate) | ! |  | ' | −! | ' | ! |\n| \u003Cbr>./) +\u003Cbr>!= \\#($%)\\#~~ ~~''* | ' |  | ∞ | ' | ∞ | ' |\n| Alternative method for multiples of 90° : Plot the 4 coordinates (0,1),(1,0), (−1,0), (0,−1) |  |  |  |  |  |  |\n| |  |  |  |  |  |  |\n| Key:\u003Cbr>(\", $) ⟹ ('() +, ),- +)\u003Cbr>This means the ! coordinate gives u","cbCaiaIR60wAUDoF","https://ap.wps.com/l/cbCaiaIR60wAUDoF","pdf",1795686,"English","# How to Use the Unit Circle\n## Reading sin and cos on the circle\n## Positive vs negative angles (anti-clockwise and clockwise)\n## Angles beyond 360°\n# Summary Tables and Memorization Patterns\n## Values for multiples of 30° and 45°\n## SOHCAHTOA method for other angles\n## Using quadrant signs for larger angles\n## Multiples of 90° using the four points","[{\"question\":\"How do you read sine and cosine values from the unit circle?\",\"answer\":\"Locate 0° as the starting point, then use the coordinates at each angle: the D coordinate gives cosine and the E coordinate gives sine. Move anti-clockwise to get values for angles from 0° to 360°.\"},{\"question\":\"What is the rule for negative angles and angles larger than 360°?\",\"answer\":\"Use clockwise motion to obtain trigonometric values for negative angles (e.g., −30° matches 330° anti-clockwise). For angles greater than 360°, keep going around the circle (e.g., 390°, 405°, 420°) to find the corresponding values.\"},{\"question\":\"How can you find trig values for larger angles without recalculating everything?\",\"answer\":\"Memorize values for key acute angles (30°, 45°, 60°, 90°) and then use SOHCAHTOA plus quadrant sign rules. For example, knowing 45° lets you determine values for 135°, 225°, and 315° by adjusting signs based on the quadrant.\"}]","Unit Circle Cheat Sheet - Trigonometric Values and Methods | PDF"]