[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523521-105":59,"doc-detail-523521-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","infinite-precalculus-graphs-of-trig-functions-worksheet-04-graphs-of-trig-functions","Infinite Precalculus Graphs of Trig Functions - Worksheet 04 - Graphs of Trig Functions","","Worksheets for Infinite Precalculus focusing on graphing trigonometric functions. Exercises ask students to determine amplitude, period in radians, phase shift, vertical shift, minimum and maximum values, and to sketch graphs using radians. Additional problems require finding period, phase shift, vertical shift, and vertical asymptotes for tangent and reciprocal trig functions, along with applying transformations from basic trig functions through stretching, translating, and reflecting.",{"@graph":69,"@context":122},[70,84,105],{"@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/infinite-precalculus-graphs-of-trig-functions-worksheet-04-graphs-of-trig-functions/523521/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/infinite-precalculus-graphs-of-trig-functions-worksheet-04-graphs-of-trig-functions/523521.png","ImageObject",300,407,{"name":92,"@type":93},"dhado","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What quantities must be found for each sine or cosine graph?","Question",{"text":112,"@type":113},"Find the amplitude, the period in radians, the phase shift in radians, the vertical shift, and the minimum and maximum values, then sketch using radians.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What extra information is required for tangent and reciprocal trig function graphs?",{"text":117,"@type":113},"Find the period in radians, the phase shift, the vertical shift, and any vertical asymptotes, then sketch the graph using radians.",{"name":119,"@type":110,"acceptedAnswer":120},"How do you solve the transformation problems in this worksheet?",{"text":121,"@type":113},"Start with a basic trig function and apply the required vertical stretch and translations (left/right/up/down) to obtain the target graph.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},523521,1791732263,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":52,"preview_page_count":4},5909893218464,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Kuta Software-Infinite Precalculus Graphs ofTrig Functions  \nName  Date  Period   \nFind the amplitude, the period in radians, the phase shift in radians, the vertical shift, and the minimum and maximum values. Then sketch the graph using radians.  \n1) y 􀀠 􀀖sin ( 􀁔 􀀐 ~~ ~~􀀘~~ ~~)  \n3) y 􀀠 􀀕sin (􀀐􀀖􀁔 􀀐 ~~ ~~) 􀀎 􀀕  \n2) y 􀀠 􀀖 cos 􀁔  \n4) y 􀀠 cos (~~ ~~􀁔􀀗 􀀎 ~~ ~~) 􀀐 􀀕  \nFind the period in radians, the phase shift in radians, the vertical shift, and two vertical asymptotes (if any). Then sketch the graph using radians.  \n5) y 􀀠 tan (􀀕􀁔 􀀐 ~~ ~~􀀔~~ ~~􀀔􀀙􀁓~~ ~~) 􀀐 􀀔  \n7) y 􀀠 􀀔􀀕 􀂘 csc (~~ ~~􀁔􀀕 􀀎 ~~ ~~􀀖􀁓􀀗~~ ~~)  \n6) y 􀀠 􀀕 cot (~~ ~~􀁔􀀖 􀀎 ~~ ~~􀀘~~ ~~)  \n8) y 􀀠 􀀖 sec (~~ ~~􀁔􀀕 􀀐 ~~ ~~􀀖􀁓􀀗~~ ~~)  \nFind the transformations required to obtain the graph starting with a basic trig function.  \n9) y 􀀠 􀀘cos ( 􀁔 􀀎 ~~ ~~􀀘~~ ~~) 10) y 􀀠 􀀘 􀀎 sin (􀀛􀁔 􀀎 ~~ ~~􀀖􀁓􀀗~~ ~~)  \n11) y 􀀠 sin ( 􀁔 􀀐 ~~ ~~) 􀀐 􀀕 12) y 􀀠 ~~ ~~􀀔􀀔􀀓 􀂘 tan ( 􀁔 􀀐 ~~ ~~)  \nKuta Software-Infinite Precalculus Graphs ofTrig Functions  \nName  Date  Period   \nFind the amplitude, the period in radians, the phase shift in radians, the vertical shift, and the minimum and maximum values. Then sketch the graph using radians.  \n1) y 􀀠 􀀖sin ( 􀁔 􀀐 ~~ ~~􀀘~~ ~~)  \n3) y 􀀠 􀀕sin (􀀐􀀖􀁔 􀀐 ~~ ~~) 􀀎 􀀕  \nAmplitude: 􀀖  \nPeriod: 􀀕􀁓  \nPhase shift: Right ~~ ~~􀀘~~ ~~  \nVert. shift: None  \nMin: 􀀐􀀖  \nMax: 􀀖  \nAmplitude: 􀀕􀀕􀁓   \nPeriod:  \n􀀖 Phase shift: Left ~~ ~~~~ ~~  \nVert. shift: Up 􀀕  \nMin: 􀀓  \nMax: 􀀗  \n2) y 􀀠 􀀖 cos 􀁔  \nAmplitude: 􀀖  \nPeriod: 􀀕􀁓  \nPhase shift: None  \nVert. shift: None  \nMin: 􀀐􀀖  \nMax: 􀀖  \n4) y 􀀠 cos (~~ ~~􀁔􀀗 􀀎 ~~ ~~) 􀀐 􀀕  \nAmplitude: 􀀔  \nPeriod: 􀀛􀁓  \nPhase shift: Left 􀁓  \nVert. shift: Down 􀀕  \nMin: 􀀐􀀖  \nMax: 􀀐􀀔  \nFind the period in radians, the phase shift in radians, the vertical shift, and two vertical asymptotes (if any). Then sketch the graph using radians.  \nPeriod:  􀁓 􀀕  \n 􀀔􀀔􀁓  Phase shift: Right  \n􀀔􀀕 Vert. shift: Down 􀀔  \nVert asym: x 􀀠  􀀚􀁓 􀀙  \n􀀕􀁓  x 􀀠 􀀖  \nPeriod: 􀀗􀁓  \nPhase shift: Left ~~ ~~􀀖􀁓􀀕~~ ~~  \nVert. shift: None  􀀖􀁓   \nVert asym: x 􀀠 􀀐 􀀕  \nx 􀀠  \n 􀁓   \n􀀕  \n6) y 􀀠 􀀕 cot (~~ ~~􀁔􀀖 􀀎 ~~ ~~􀀘~~ ~~)  \n8) y 􀀠 􀀖 sec (~~ ~~􀁔􀀕 􀀐 ~~ ~~􀀖􀁓􀀗~~ ~~)  \nFind the transformations required to obtain the graph starting with a basic trig function.  \n9) y 􀀠 􀀘cos ( 􀁔 􀀎 ~~ ~~􀀘~~ ~~)  \n11) y 􀀠 sin ( 􀁔 􀀐 ~~ ~~) 􀀐  \nStarting with cos 􀁔 , vertically stretch by 􀀘 , translate left ~~ ~~􀀘~~ ~~  \n􀀕 Starting with sin 􀁔, translate right ~~ ~~~~ ~~,  \ntranslate down 􀀕  \n10) y 􀀠 􀀘 􀀎 sin (􀀛􀁔 􀀎 ~~ ~~􀀖􀁓􀀗~~ ~~) Starhoring wontalilthyssinhrin􀁔k, by ~~ ~~􀀔􀀛~~ ~~, translate left ~~ ~~􀀖􀀖~~ ~~, translate up 􀀘  \n12) y 􀀠 ~~ ~~􀀔􀀔􀀓 􀂘 tan ( 􀁔 􀀐 ~~ ~~) Startvertingallwythhritannk􀁔by, ~~ ~~􀀔􀀔􀀓~~ ~~ , translate right ~~ ~~~~ ~~  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaiiRhdj3DPRAm","https://ap.wps.com/l/cbCaiiRhdj3DPRAm","pdf",67885,"English","# Find Key Graph Features\n## Sine and Cosine Graphs\n## Tangent and Reciprocal Trig Graphs\n# Determine Transformations\n## From Basic Trig Functions","[{\"question\":\"What quantities must be found for each sine or cosine graph?\",\"answer\":\"Find the amplitude, the period in radians, the phase shift in radians, the vertical shift, and the minimum and maximum values, then sketch using radians.\"},{\"question\":\"What extra information is required for tangent and reciprocal trig function graphs?\",\"answer\":\"Find the period in radians, the phase shift, the vertical shift, and any vertical asymptotes, then sketch the graph using radians.\"},{\"question\":\"How do you solve the transformation problems in this worksheet?\",\"answer\":\"Start with a basic trig function and apply the required vertical stretch and translations (left/right/up/down) to obtain the target graph.\"}]","Infinite Precalculus Graphs of Trig Functions - Worksheet 04 - Graphs of Trig Functions | PDF",1791426948]