[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-572172-105":53,"doc-detail-572172-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","harolds-trigonometry-cheat-sheet-study-guide","Harold’s Trigonometry Cheat Sheet - Study Guide","","Harold’s Trigonometry Cheat Sheet provides a compact reference for trigonometric concepts centered on the unit circle and the six trig functions. It includes a quadrant-focused unit circle trig chart with degree-to-radian values and corresponding sine, cosine, and tangent patterns. The sheet also summarizes graphical transformations of y=a·sin(b(x−h))+k via six “levers” (vertical/horizontal shifts, amplitude/frequency changes, and x/y-axis reflections), plus related graphing tips and notes for interpreting parameters.",{"@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/harolds-trigonometry-cheat-sheet-study-guide/572172/",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},"Miles","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},"What values does the unit circle chart connect for common angles?","Question",{"text":102,"@type":103},"It links degree and radian measures to sine, cosine, and tangent outputs for those angles, with a focus on Quadrant I only.","Answer",{"name":105,"@type":100,"acceptedAnswer":106},"How do the six “trig levers” affect the graph of y = a sin(b(x − h)) + k?",{"text":107,"@type":103},"They control vertical translation (k), phase shift (h), amplitude (a), frequency (b), and reflections about the y-axis and x-axis (changing signs of b or a).",{"name":109,"@type":100,"acceptedAnswer":110},"What does amplitude mean for the sine or cosine graph?",{"text":111,"@type":103},"Amplitude is described as a scaling factor on the y-values, and the sheet notes that it is not the peak-to-peak distance on the y-axis.","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},572172,1791925922,{"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},13056703019404,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Harold’s Trigonometry Cheat Sheet  \n20 May 2026  \n\n| Unit Circle |  |  | Trig Chart |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| |  |  | (Quadrant I only) |  |  |  |  |  |  |  |  |  |  |\n|  |  |  |  | Degrees |  |  |  | 0° | 30° | 45° | 60° | 90° |  |\n|  |  |  |  | Radians |  |  |  | 0 | π/6 | π/4 | π/3 | π/2 |  |\n|  |  |  |  | Sin (θ) → |  |  |  | 0 | 1 2 | √2\u003Cbr>2 | √3\u003Cbr>2 | 1 |  |\n|  |  |  |  | Cos (θ) 􀃅 |  |  |  | 1 | \u003Cbr>√3\u003Cbr>2 | \u003Cbr>√2\u003Cbr>2 | 1 2 | 0 |  |\n|  |  |  |  | Sin (θ) Pattern |  |  |  | √0\u003Cbr>2 | √1\u003Cbr>2 | √2\u003Cbr>2 | √3\u003Cbr>2 | |  |\n|  |  |  |  | Tan (θ) Pattern |  |  |  | 0 | (√33)1 | ~~ ~~ 2\u003Cbr>(√3) \u003Cbr>3 | (√33)3 | Und |  |\n| Graphical Representation of the Six Trig Functions |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| \u003Cbr>\u003Cbr>3􀟨 2\u003Cbr>\u003Cbr>2\u003Cbr>\u003Cbr>π\u003Cbr>\u003Cbr>−π\u003Cbr>\u003Cbr>−􀟨 2\u003Cbr>\u003Cbr>−3􀟨 2\u003Cbr>\u003Cbr>􀟨 2\u003Cbr>\u003Cbr>“All Students Take Calculus” |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| The Six Trig “Levers” | y = a sin (b (x-h)) + k | Graphing Tips |  |  |  |  | Notes |  |  |  |  |  |  |\n| 1) Move up/down ↕ | k (Vertical translation) | 􀝇 = (􀝉􀜽􀝔~~ ~~+2~~ ~~􀝉􀝅􀝊) |  |  |  |  | If k = f(x) then x-axis is replaced by f(x)-axis |  |  |  |  |  |  |\n| 2) Move left/right ↔ | h (Phase shift) | ‘+ ‘ shifts right |  |  |  |  | sin (􀝔) = cos (􀝔 − π/2) |  |  |  |  |  |  |\n| 3) Stretch up/down ↕ | a (Amplitude) | 􀜽 = | (􀝉􀜽􀝔 − 􀝉􀝅􀝊) 2 |  |  |  | a is NOT peak-to-peak on the y-axis |  |  |  |  |  |  |\n| 4) Stretch left/right ↔ | b (Frequency ⦁ 2π) | 􀜶 = |  | 2􀟨|􀜾| | = | 1 ƒ | T = peak-to-peak on the 􀟠-axis\u003Cbr>􀜶 = |􀰗􀯕| for 􀝐􀜽􀝊 (􀜾􀝔) and 􀜿􀝋􀝐 (􀜾􀝔) |  |  |  |  |  |  |\n| 5) Flip about y-axis 􀀴 | b → –b | 􀝂 (􀝔) → 􀝂(−􀝔) |  |  |  |  | Even Function: cos (􀝔) = cos (−􀝔) |  |  |  |  |  |  |\n| 6) Flip about x-axis 􀀳 | a → –a | 􀝂 (􀝔) → −􀝂(􀝔) |  |  |  |  | Odd Function: sin (􀝔) = −sin (−􀝔) |  |  |  |  |  |  |\n\n\n| Unit Circle |  |\n| --- | --- |\n| (􀝔, 􀝕) = (􀜿􀝋􀝏 􀟠 , 􀝏􀝅􀝊 􀟠) | 􀟨 􀝎􀜽􀝀 = 180⁰ |\n\nSource: Unit Circle Quick Lesson-Matter of Math [https://matterofmath.com/trigonometry/unit-circle/](https://matterofmath.com/trigonometry/unit-circle/)","cbCaiqE9P1Gql5ug","https://ap.wps.com/l/cbCaiqE9P1Gql5ug","pdf",529093,"English","# Unit Circle Reference\n## Degree and Radian Values\n## Trig Function Values\n# Graphing the Six Trig Functions\n## The Six Trig \"Levers\"\n## Graphing Tips and Notes","[{\"question\":\"What values does the unit circle chart connect for common angles?\",\"answer\":\"It links degree and radian measures to sine, cosine, and tangent outputs for those angles, with a focus on Quadrant I only.\"},{\"question\":\"How do the six “trig levers” affect the graph of y = a sin(b(x − h)) + k?\",\"answer\":\"They control vertical translation (k), phase shift (h), amplitude (a), frequency (b), and reflections about the y-axis and x-axis (changing signs of b or a).\"},{\"question\":\"What does amplitude mean for the sine or cosine graph?\",\"answer\":\"Amplitude is described as a scaling factor on the y-values, and the sheet notes that it is not the peak-to-peak distance on the y-axis.\"}]","Harold’s Trigonometry Cheat Sheet - Study Guide | PDF"]