[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-detail-467559-en":59,"doc-seo-467559-105":80},{"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":5,"data":60},{"doc_id":61,"user_id":62,"nickname":63,"user_avatar":64,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":66,"doc_content":67,"file_id":68,"file_url":69,"file_type":70,"file_size":71,"view_count":24,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":72,"language":73,"language_code":74,"site_id":75,"html_lang":74,"table_of_contents":76,"faqs":77,"seo_title":78,"seo_description":66,"update_tm":79,"read_time":39},467559,687197207639,"Asher","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Rotating Around Axis - Rotation Formula Practice","Worksheet and answer key focused on rotating two-dimensional shapes around a fixed point using angle-of-rotation notation. It provides the rotation formula for converting original coordinates (x, y) into new coordinates (x1, y1) using cos(θ) and sin(θ). The content includes a worked example for a 60° rotation from (1,4) and asks learners to compute coordinates for multiple specified rotations such as 255°, 95°, -55°, and -34°.","Rotating Around Axis  \nName:  \nII I  \nIII IV  \nII I  \nIII IV  \nII I  \nIII IV  \nII I  \nIII IV  \nRotate each shape. Answer with the new coordinates.  \nθ = Angle of Rotation  \nRotation Formula  \nx1 = x×cos(θ) -y×sin(θ)  \ny1 = x×sin(θ) + y×cos(θ)  \nIn the example to the right the shape is at coordinates (1,4) . Lets find the coordinates if we rotated the shape 60° .  \n1. x1 = 1×cos(60) -4×sin(60) y1 = 1×sin(60) + 4×cos(60)  \n2. x1 = 1×0 .5-4×0 .87 y1 = 1×0.87 + 4×0.5  \n3. x1 = 0.5-3.48 y1 = 0.87 + 2  \n4. x1 = -2.98 y1 = 2.87  \n5. Looking at shape, we can see that rotated 60° it is at  \n(-2 .98 , 2 .87) .  \nAnswers  \n1.  \n2.  \n3.  \n4.  \n1) Rotate the shape 255° around the point 2) Rotate the shape 95° around the point (0,0) . (0,0) .  \n3) Rotate the shape-55° around the point 4) Rotate the shape-34° around the point (0,0) . (0,0) .  \n[Math](Math www.CommonCoreSheets.com 10 1-4)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 10 1-4)[ 10](Math www.CommonCoreSheets.com 10 1-4)[ 1-4](Math www.CommonCoreSheets.com 10 1-4) 75 50 25 0  \nRotating Around Axis  \nName: Answer Key  \n\n| \u003Cbr>Rotate each shape. Answer with the new coordinates.\u003Cbr>θ = Angle of Rotation\u003Cbr>Rotation Formula\u003Cbr>x1 = x×cos(θ) -y×sin(θ)\u003Cbr>y1 = x×sin(θ) + y×cos(θ)\u003Cbr>In the example to the right the shape is at coordinates (1,4) . Lets find the coordinates if we rotated the shape 60° .\u003Cbr>\u003Cbr>1. x1 = 1×cos(60) -4×sin(60) y1 = 1×sin(60) + 4×cos(60)\u003Cbr>2. x1 = 1×0 .5-4×0 .87 y1 = 1×0.87 + 4×0.5\u003Cbr>3. x1 = 0.5-3.48 y1 = 0.87 + 2\u003Cbr>4. x1 = -2.98 y1 = 2.87\u003Cbr>5. Looking at shape, we can see that rotated 60° it is at\u003Cbr>(-2 .98 , 2 .87) .\u003Cbr>|  | Answers 1.  (2.6,1.7) \u003Cbr>2.  (6.5,-6.6)  3.  (-6.3,3.2)  4.  (1.3,6.9)  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- |\n| 1) Rotate the shape 255° around the point (0,0) . | 2) Rotate the shape 95° around the point (0,0) .\u003Cbr>\u003Cbr>4) Rotate the shape-34° around the point (0,0) . |  |  |  |  |  |\n| (1 )\u003Cbr>II I\u003Cbr>III IV\u003Cbr>|  |  |  |  |  |  |\n| 3) Rotate the shape-55° around the point (0,0) .\u003Cbr>(- 1, -7 )\u003Cbr>II I\u003Cbr>III IV\u003Cbr>|  |  |  |  |  |  |\n|  | |  |  |  |  |  |\n|  |  |  |  |  |  |  |\n\n[Math](Math www.CommonCoreSheets.com 10 1-4)[ www.CommonCoreSheets.com](Math www.CommonCoreSheets.com 10 1-4)[ 10](Math www.CommonCoreSheets.com 10 1-4)[ 1-4](Math www.CommonCoreSheets.com 10 1-4) 75 50 25 0  \nRotating Around Axis  \nName:  \n\n| \u003Cbr>Rotate each shape. Answer with the new coordinates.\u003Cbr>θ = Angle of Rotation\u003Cbr>Rotation Formula\u003Cbr>x1 = x×cos(θ) -y×sin(θ)\u003Cbr>y1 = x×sin(θ) + y×cos(θ)\u003Cbr>In the example to the right the shape is at coordinates (1,4) . Lets find the coordinates if we rotated the shape 60° .\u003Cbr>\u003Cbr>1. x1 = 1×cos(60) -4×sin(60) y1 = 1×sin(60) + 4×cos(60)\u003Cbr>2. x1 = 1×0 .5-4×0 .87 y1 = 1×0.87 + 4×0.5\u003Cbr>3. x1 = 0.5-3.48 y1 = 0.87 + 2\u003Cbr>4. x1 = -2.98 y1 = 2.87\u003Cbr>5. Looking at shape, we can see that rotated 60° it is at\u003Cbr>(-2 .98 , 2 .87) .\u003Cbr>|  | Answers\u003Cbr>1.  \u003Cbr>2.   |\n| --- | --- | --- |\n| 1) Rotate the shape 255° around the point (0,0) .\u003Cbr>\u003Cbr>II I\u003Cbr>III IV\u003Cbr>| 2) Rotate the shape 95° around the point (0,0) .\u003Cbr>\u003Cbr>II I\u003Cbr>III IV\u003Cbr>|  |\n\nMath  \nModified  \n[www.CommonCoreSheets.com](www.CommonCoreSheets.com)  \n10  \n1-2 50 0  \n\n|  |  |\n| --- | --- |","cbCaigI6iVPl8xix","https://ap.wps.com/l/cbCaigI6iVPl8xix","pdf",55431,3,"English","en",105,"# Rotate each shape\n## Angle of Rotation and Rotation Formula\n## Example: Rotating 60°\n## Practice Answers","[{\"question\":\"What rotation formula is used to find the new coordinates after rotating a point?\",\"answer\":\"The worksheet uses x1 = x·cos(θ) - y·sin(θ) and y1 = x·sin(θ) + y·cos(θ). These convert original coordinates (x, y) into rotated coordinates (x1, y1).\"},{\"question\":\"In the example, what are the starting coordinates and the result after rotating 60°?\",\"answer\":\"The example starts with coordinates (1,4) and rotates by 60°. The resulting coordinates shown are (-2.98, 2.87).\"},{\"question\":\"Which rotation tasks are included in the answer section?\",\"answer\":\"The answer section includes rotations around specific points using angles such as 255° around (0,0), 95° around (0,0), -55° around (0,0), and -34° around (0,0), asking for the new coordinates.\"}]","Rotating Around Axis - Rotation Formula Practice | PDF",1790773002,{"code":4,"msg":81,"data":82},"ok",{"site_id":75,"language":74,"slug":83,"title":65,"keywords":84,"description":66,"schema_data":85,"social_meta":138,"head_meta":140,"extra_data":142,"updated_unix":143},"rotating-around-axis-rotation-formula-practice","",{"@graph":86,"@context":137},[87,100,120],{"@type":88,"itemListElement":89},"BreadcrumbList",[90,94,96,98],{"item":91,"name":92,"@type":93,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":95,"name":9,"@type":93,"position":14},"https://docshare.wps.com/document/",{"item":97,"name":20,"@type":93,"position":72},"https://docshare.wps.com/document/exam/",{"item":99,"name":65,"@type":93,"position":19},"https://docshare.wps.com/document/rotating-around-axis-rotation-formula-practice/467559/",{"url":99,"name":65,"@type":101,"image":102,"author":107,"headline":65,"publisher":109,"fileFormat":112,"inLanguage":74,"description":66,"dateModified":113,"datePublished":114,"encodingFormat":112,"isAccessibleForFree":115,"interactionStatistic":116},"DigitalDocument",{"url":103,"@type":104,"width":105,"height":106},"https://docshare.wps.com/thumbnails/rotating-around-axis-rotation-formula-practice/467559.png","ImageObject",300,407,{"name":63,"@type":108},"Person",{"url":91,"name":110,"@type":111},"DocShare","Organization","application/pdf","2026-10-31","2026-09-30",true,{"@type":117,"interactionType":118,"userInteractionCount":24},"InteractionCounter",{"@type":119},"ViewAction",{"@type":121,"mainEntity":122},"FAQPage",[123,129,133],{"name":124,"@type":125,"acceptedAnswer":126},"What rotation formula is used to find the new coordinates after rotating a point?","Question",{"text":127,"@type":128},"The worksheet uses x1 = x·cos(θ) - y·sin(θ) and y1 = x·sin(θ) + y·cos(θ). These convert original coordinates (x, y) into rotated coordinates (x1, y1).","Answer",{"name":130,"@type":125,"acceptedAnswer":131},"In the example, what are the starting coordinates and the result after rotating 60°?",{"text":132,"@type":128},"The example starts with coordinates (1,4) and rotates by 60°. The resulting coordinates shown are (-2.98, 2.87).",{"name":134,"@type":125,"acceptedAnswer":135},"Which rotation tasks are included in the answer section?",{"text":136,"@type":128},"The answer section includes rotations around specific points using angles such as 255° around (0,0), 95° around (0,0), -55° around (0,0), and -34° around (0,0), asking for the new coordinates.","https://schema.org",{"og:url":99,"og:type":139,"og:title":65,"og:site_name":110,"og:description":66},"article",{"robots":141,"canonical":99},"index,follow",{"doc_id":61,"site_id":75},1792925839]