[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-434876-105":59,"doc-detail-434876-en":131},{"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":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","38-the-tangent-function-38-test-prep","3.8 The Tangent Function - 3.8 Test Prep","","Worksheet-style math practice focused on the tangent function and trigonometric equations. It includes directions to write equations representing all asymptotes, determine slopes related to terminal rays, and evaluate multiple tangent expressions. Several problems ask to graph tangent functions and solve for parameters or x-values using vertical asymptotes and given solutions for equations of the form y = a·tan(bx) (with constants).",{"@graph":69,"@context":123},[70,84,106],{"@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/38-the-tangent-function-38-test-prep/434876/",{"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/38-the-tangent-function-38-test-prep/434876.png","ImageObject",300,407,{"name":92,"@type":93},"EvelynWrites","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-23","2026-09-29",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",13,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How do you write an equation representing all asymptotes of a tangent graph?","Question",{"text":113,"@type":114},"Use the period and horizontal shift to identify where the tangent function is undefined (where cosine is 0). Those x-values form the vertical asymptotes.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What determines the slope of the terminal ray for an angle in standard position?",{"text":118,"@type":114},"For an angle in standard position, the terminal ray’s slope is given by the tangent of the angle, using the relationship between slope and tangent.",{"name":120,"@type":111,"acceptedAnswer":121},"How are solutions to an equation like tan(bx)=value found?",{"text":122,"@type":114},"First find the reference angle whose tangent equals the given value, then generate all x-values by adding multiples of the tangent period and accounting for any vertical asymptotes or transformations.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},434876,1790816678,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":81,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":39},687212989558,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Write an equation that represents all asymptotes of the graph of 􀢌 in the 􀢞􀢟-plane.   \n\n| 1. 􀝂ሺ􀟠ሻ ൌ tanሺ3􀟠ሻ\u003Cbr>| |  | 2. 􀝂ሺ􀟠ሻ ൌ tanሺ6􀟠ሻ |  |  | 3. 􀝂ሺ􀟠ሻ ൌ tan ቀఏହቁ\u003Cbr>\u003Cbr>| |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  | | | |  |  |  |\n| 􀟠 ൌ గ଺ ൅􀝇 గଷ, for integer values of 􀝇 . |  |  |  |  |  |  |  |  |\n|  |  |  | 􀟠 ൌ గଵଶ ൅􀝇 గ଺, for integer values of 􀝇 . |  |  |  |  |  |\n|  |  |  |  |  |  | 􀟠 ൌ ହగଶ ൅􀝇5􀟨 , for integer values of 􀝇 . |  |  |\n|  |  |  |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  |  |\n| In the 􀢞􀢟-plane, the angle 􀣂 is in standard position. What is the slope of the terminal ray of the angle? |  |  |  |  |  |  |  |  |\n\n5. 􀟠 ൌ  \nଷగ  \nସ  \n6. 􀟠 ൌ  \nହగ  \nଷ  \n© The Algebros [from FlippedMath.com](from FlippedMath.com)  \nEvaluate.  \n7. tan గଶ 8. tan ସగଷ 9. tan ହగସ 10. tan ଵଵగ  \n଺  \n11. 􀝕 ൌ െ ଵଶ tan 􀟠 12. 􀝕 ൌ 4tan ቀଵଶ 􀟠 ቁ െ 3  \n13. 􀝕 ൌ 2tan ቀ􀟠 െ గସቁ െ 1 14. 􀝕 ൌ tanሺ2􀟠 ൅ 􀟨ሻ ൅ 2  \nGraph each trig function.  \n3.8 The Tangent Function  3.8 Test Prep   \n15. The graph of the function 􀝃 is given in the 􀝔􀝕-plane. If  \n􀝃ሺ􀝔ሻ ൌ 􀜽 tanሺ􀜾􀝔ሻ െ 20, where 􀜽 and 􀜾 are constants, which of the following could be true?  \nI. If 􀜽 ൐ 0 then 􀜾 ൐ 1  \nII. If 􀜽 ൐ 0 then 􀜾 ൏ 0  \nIII. If 􀜽 ൏ 0 then 􀜾 ൐ 1  \nIV. If 􀜽 ൏ 0 then 􀜾 ൏ 0  \n(A) III only (B) IV only  \n(C) I and IV only (D) II and III only  \n© The Algebros [from FlippedMath.com](from FlippedMath.com)  \n16. The graph of 􀝂ሺ􀝔ሻ ൌ tanሺ􀜾􀝔ሻ, where 􀜾 is a constant, is shown in the 􀝔􀝕-plane. What is the value of 􀜾?  \n17. The figures shows the graph of 􀝂ሺ􀝔ሻ ൌ 􀜽 tanሺ􀜾􀝔ሻ, where 􀜽 and  \n􀜾 are constants, in the 􀝔􀝕-plane. The graph of 􀝂 has two vertical asymptotes at 􀝔 ൌ െ􀟨 and 􀝔 ൌ 􀟨 , and a point with coordinates given is on the graph of 􀝂 . What are all solutions to 􀝂ሺ􀝔ሻ ൌ 1.829?  \n(A) 􀝔 ൌ 2.317 only  \n(B) 􀝔 ൌ 2.317 ൅􀟨􀝇 , where 􀝇 is any integer  \n(C) 􀝔 ൌ 2.317 ൅ 2􀟨􀝇 , where 􀝇 is any integer  \n(D) 􀝔 ൌ 2.317 ൅ 3􀟨􀝇 , where 􀝇 is any integer Graph of 􀝂  \n© The Algebros [from FlippedMath.com](from FlippedMath.com)","cbCaidvMNsRXFDW6","https://ap.wps.com/l/cbCaidvMNsRXFDW6","pdf",977661,"English","# Write asymptotes and slopes\n## Tangent equation representations and terminal ray slope\n# Evaluate and solve tangent problems\n## Evaluate tangent expressions\n## Determine parameters and solve y = 1.829","[{\"question\":\"How do you write an equation representing all asymptotes of a tangent graph?\",\"answer\":\"Use the period and horizontal shift to identify where the tangent function is undefined (where cosine is 0). Those x-values form the vertical asymptotes.\"},{\"question\":\"What determines the slope of the terminal ray for an angle in standard position?\",\"answer\":\"For an angle in standard position, the terminal ray’s slope is given by the tangent of the angle, using the relationship between slope and tangent.\"},{\"question\":\"How are solutions to an equation like tan(bx)=value found?\",\"answer\":\"First find the reference angle whose tangent equals the given value, then generate all x-values by adding multiples of the tangent period and accounting for any vertical asymptotes or transformations.\"}]","3.8 The Tangent Function - 3.8 Test Prep | PDF",1790670923]