[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-207507-105":59,"doc-detail-207507-en":124},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":117,"head_meta":119,"extra_data":121,"updated_unix":123},105,"en","aqa-gcse-further-maths-trigonometric-graphs-equations-revision-notes","AQA GCSE Further Maths - Trigonometric Graphs & Equations - Revision Notes","","AQA GCSE Further Maths revision notes focused on trigonometric graphs and equations, explaining what graphs of y=sin x, y=cos x and y=tan x represent and why their shapes matter. The material guides sketching trig graphs using a consistent pattern with a starting point and changes every 90°. It also details key properties such as periodicity, period, ranges, amplitudes, symmetry, and tangent asymptotes, supported by a worked example and emphasis on labeling key values.",{"@graph":69,"@context":116},[70,84,99],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/aqa-gcse-further-maths-trigonometric-graphs-equations-revision-notes/207507/",{"url":83,"name":65,"@type":85,"author":86,"headline":65,"publisher":89,"fileFormat":92,"inLanguage":63,"description":67,"dateModified":93,"datePublished":93,"encodingFormat":92,"isAccessibleForFree":94,"interactionStatistic":95},"DigitalDocument",{"name":87,"@type":88},"Hazel","Person",{"url":74,"name":90,"@type":91},"DocShare","Organization","application/pdf","2026-09-05",true,{"@type":96,"interactionType":97,"userInteractionCount":4},"InteractionCounter",{"@type":98},"ViewAction",{"@type":100,"mainEntity":101},"FAQPage",[102,108,112],{"name":103,"@type":104,"acceptedAnswer":105},"What do graphs of trigonometric functions (sin, cos, tan) show?","Question",{"text":106,"@type":107},"They show how y values change as angles change, using specific equations for y=sin x, y=cos x, and y=tan x. The notes explain that trig graphs are used to model wave-like behaviour in mathematics applications.","Answer",{"name":109,"@type":104,"acceptedAnswer":110},"How do you sketch trigonometric graphs quickly?",{"text":111,"@type":107},"Sketching follows a pattern: identify the starting point, then apply what changes every 90°. The notes recommend marking key values and joining them smoothly, then labeling the curve with its equation.",{"name":113,"@type":104,"acceptedAnswer":114},"What key properties should you know for y=sin x, y=cos x, and y=tan x?",{"text":115,"@type":107},"The notes cover periodicity and period, the ranges for sin and cos (between -1 and 1), amplitude, and symmetry for sin and cos. For tan, the notes highlight repeating every 180° and the presence of vertical asymptotes (discontinuities).","https://schema.org",{"og:url":83,"og:type":118,"og:title":65,"og:site_name":90,"og:description":67},"article",{"robots":120,"canonical":83},"index,follow",{"doc_id":122,"site_id":62},207507,1788599800,{"code":4,"msg":5,"data":125},{"doc_id":122,"user_id":126,"nickname":87,"user_avatar":127,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":128,"file_id":129,"file_url":130,"file_type":131,"file_size":132,"view_count":4,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":133,"language":134,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":135,"faqs":136,"seo_title":137,"seo_description":67,"update_tm":123,"read_time":138},137441390410,"https://ap-avatar.wpscdn.com/avatar/2000252f4ab5702993?_k=1776741390130283984","Head to www.savemyexams. com for more awesome resources  \n AQA GCSE Further Maths  \nTrigonometric Graphs & Equations  \nContents  \n Trigonometric Graphs  \n Trigonometric Identities  Solving Trig Equations  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nYour notes  \nHead to www.savemyexams. com for more awesome resources  \nTrigonometric Graphs  \nGraphs of Trigonometric Functions  \nWhat is meant by graphs of trigonometric functions?  \n The graphs are  \n y = sin x  \n y = cos x  \n y = tan x  \nWhy do I need to know what graphs of trigonometric functions look like?  \n Trigonometric graphs (trig graphs) are used in various applications of mathematics  \n e. g. the oscillating / wave-like nature of sine and/or cosine can be used to model how a pendulum swings or tide heights  \nHow do I sketch trig graphs?  \n As with other graphs, being familiar with the general style of trig graphs will help you sketch them quickly  \n They can then be used to |nd values or angles alongside, or instead of, your calculator  \n All trig graphs follow a pattern – a “starting point” and then “something happens every 90°”  \n The diagrams below show the graphs of sin, cosand tan from-360° to 360°  \n Most questions will focus on the postive part of the graph for angles between 0° and 360°  \nYour notes  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nHead to www.savemyexams. com for more awesome resources  \nYour notes  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nHead to www.savemyexams. com for more awesome resources  \nYour notes  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nHead to www.savemyexams. com for more awesome resources  \nYour notes  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nHead to www.savemyexams. com for more awesome resources  \n Worked example  \nOn the axes provided, sketch the graphofy = sin x ° for 0 ≤x ≤360 .  \nMark key values on the axes provided; 1and −1 on they-axis and 90 , 180 , 270 and 360 onthex-axis Try to space them evenly apart but also remember this is a sketch!  \nstarts at (0 , 0) then every 90° it cycles though 1 , 0 , −1 , 0 , ...  \nMark these points on the axes  \nFinally, join the points with a smooth curve  \nYou will get better at this with practice but again remember it is a sketch so do not spend ages making it look perfect!  \nIt is best practice to label the curve with its equation  \nYour notes  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nHead to www.savemyexams. com for more awesome resources  \nYour notes  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topic Questions, Past Papers  \nHead to www.savemyexams. com for more awesome resources  \nProperties of Trigonometric Graphs  \nWhat is meant by the properties of trigonometric graphs?  \n Properties refers to any special features or patterns  \n The graphs y = sin x, y = cos x andy = tan x are all periodic  \n This means their graphs/curves repeat every so often  \n The frequency (rate) at which they repeat is called the period  \nWhat are the properties of the graph y = sin x?  \n Angles will always be onthex-axis  \n Values of sine run between-1 and 1  \n So they-axis will only need to run between-1 and 1  \n You may see this referred toasthe range of y = sin x ( −1 ≤y ≤ 1 )  \n The graph y = sin x repeats every 360° (has period 360)  \n The graph 'starts' at (0 , 0) (but can have negative angles too)  \n 'Something ' happens every 90°  \n y = sin x cycles between 0 , 1 , 0 , -1 , 0 , 1 , 0 , -1 , ...  \n . .. every 90° starting at (0 , 0)  \n Other properties of the the graph ofy = sin x that can be helpful but do not crop up often include  \n y = sin x has rotational symmetry around the origin  \n The graph has an amplitude of 1  \n Amplitude means the height of the sine graph above zero  \nYour notes  \n© 2015 − 2024 Save My Exams, Ltd. · Revision Notes, Topi","cbCaigwcAQVA0CRa","https://ap.wps.com/l/cbCaigwcAQVA0CRa","pdf",2855105,29,"English","# Trigonometric Graphs\n## Graphs of Trigonometric Functions\n## How to Sketch Trig Graphs\n## Worked Example: Sketch y=sin x\n# Properties of Trigonometric Graphs\n## Periodic Properties of sin, cos, tan\n## Properties of y=sin x\n## Properties of y=cos x\n## Properties of y=tan x","[{\"question\":\"What do graphs of trigonometric functions (sin, cos, tan) show?\",\"answer\":\"They show how y values change as angles change, using specific equations for y=sin x, y=cos x, and y=tan x. The notes explain that trig graphs are used to model wave-like behaviour in mathematics applications.\"},{\"question\":\"How do you sketch trigonometric graphs quickly?\",\"answer\":\"Sketching follows a pattern: identify the starting point, then apply what changes every 90°. The notes recommend marking key values and joining them smoothly, then labeling the curve with its equation.\"},{\"question\":\"What key properties should you know for y=sin x, y=cos x, and y=tan x?\",\"answer\":\"The notes cover periodicity and period, the ranges for sin and cos (between -1 and 1), amplitude, and symmetry for sin and cos. For tan, the notes highlight repeating every 180° and the presence of vertical asymptotes (discontinuities).\"}]","AQA GCSE Further Maths - Trigonometric Graphs & Equations - Revision Notes | PDF",73]