[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-314252-105":59,"doc-detail-314252-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","pre-calculus-reference-sheet-factoring-analytic-geometry","Pre-Calculus Reference Sheet - Factoring & Analytic Geometry","","Pre-Calculus Reference Sheet consolidates core algebra and trigonometry formulas for quick review. It covers key factoring identities, analytic geometry relationships (slope, line equation, distance), and exponent and logarithm rules. It summarizes arithmetic and geometric series expressions, then provides a comprehensive set of trigonometric angle values, right-triangle definitions, and identity groups (Pythagorean, reciprocal, ratio, sum/difference, double/half/triple, and power reduction).",{"@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/pre-calculus-reference-sheet-factoring-analytic-geometry/314252/",{"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/pre-calculus-reference-sheet-factoring-analytic-geometry/314252.png","ImageObject",300,407,{"name":92,"@type":93},"Jasmine","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-09-20",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",17,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What factoring identities are included in the reference sheet?","Question",{"text":113,"@type":114},"It lists common products and squares such as a2 − b2 = (a − b)(a + b), and (a ± b)2 forms, plus sum/difference of cubes expansions for a3 + b3 and a3 − b3.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Which analytic geometry formulas are provided?",{"text":118,"@type":114},"The sheet includes slope m = (y2 − y1)/(x2 − x1), the point-slope form y − y1 = m(x − x1), and a distance formula d based on the coordinate differences.",{"name":120,"@type":111,"acceptedAnswer":121},"What trigonometry identity categories are covered?",{"text":122,"@type":114},"It provides right-triangle ratio definitions (sin, cos, tan), Pythagorean identities, reciprocal and ratio identities, sum-and-difference identities, double-angle, half-angle, triple-angle, power-reduction, and product-to-sum forms.","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},314252,1789962514,{"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":14,"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":24,"preview_page_count":4},2336478487870,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Pre-Calculus Reference Sheet  \nFactoring  \n• a2 − b2 = (a − b)(a + b)  \n• a2 + b2 is prime  \n• a2 + 2ab + b2 = (a + b)2  \n• a2 − 2ab + b2 = (a − b)2  \n• a3 + b3 = (a + b) 􀀀a2 − ab + b2 􀀁  \n• a3 − b3 = (a − b) 􀀀a2 + ab + b2 􀀁  \n\n| Analytic Geometry\u003Cbr>• slope: m = y~~ ~~2x~~ ~~2~~ ~~−~~ ~~yx11\u003Cbr>• equation of a line: y − y 1 = m (x − x1 )\u003Cbr>• distance: d = q (x2 − x1 )2 + (y2 − y1 )2 |\n| --- |\n| Exponent Rules\u003Cbr>• ax+y = ax ay\u003Cbr>• (ab)x = axbx\u003Cbr>• (ax )y = axy\u003Cbr>• a0 = 1 if a  0\u003Cbr>• a−x = a1x if a  0\u003Cbr>• ax−y = axay if a  0 |\n| Logarithm Rules\u003Cbr>• logb x = y ⇐⇒ x = by\u003Cbr>• blogb x = x\u003Cbr>• logb bx = x\u003Cbr>• logb 1 = 0\u003Cbr>• logb b = 1\u003Cbr>• logb xy = logb x + logb y x\u003Cbr>• logb y = logb x − logb y\u003Cbr>• logb xy = y logb x\u003Cbr>• log x = loga xb loga b |\n\nArithmetic Series  \n• ak = a + (k − 1)dn n  \n• Sn = X [a + (k − 1)d] = 2 [2a + (n − 1)d] k=1  \n• Sn = 1 [a + (k − 1)d] = n 􀀒 a~~ ~~an 􀀓  \nGeometric Series  \n• an = arn−1  \nn−1  \n• Sn = X ark k=0  \n= a 􀀔 ~~ ~~11rnr 􀀕  \nif r  1  \n∞ a  \n• S = X ark = 1 − r if |r| \u003C 1 k=0  \nTrigonometry  \nadjacent opposite  \n• cos A = ~~ ~~ • sinA = ~~ ~~  \nhypotenuse hypotenuse  \nopposite  \n• tanA = ~~ ~~  \nadjacent  \n\n|  | 0◦ | 30◦ | 45◦ | 60◦ | 90◦ |\n| --- | --- | --- | --- | --- | --- |\n|  | 0 | π 6 | π 4 | π 3 | π 2 |\n\n\n| sin | 0 | 1 2 | √2\u003Cbr>2 | √3\u003Cbr>2 | 1 |\n| --- | --- | --- | --- | --- | --- |\n| cos | 1 | √3\u003Cbr>2 | √2\u003Cbr>2 | 1 2 | 0 |\n| tan | 0 | √3\u003Cbr>3 | 1 | √3 | undefined |\n\n\n| Pythagorean Identities\u003Cbr>• cos2 A + sin2 A = 1\u003Cbr>• 1 + tan2 A = sec2 A\u003Cbr>• 1 + cot2 A = csc2 A |\n| --- |\n| Ratio Identities\u003Cbr>• tanA = sin~~ ~~Acos~~ ~~A • cotA = csosinAA |\n\nReciprocal Identities  \n• sec A = co1sA • csc A = si1nA • cotA = ta1n~~ ~~A  \n\n| Sum and Difference Identities\u003Cbr>• cos(A ± B) = cos A cos B ∓ sinAsinB\u003Cbr>• sin(A ± B) = sinA cos B ± cos A sin B\u003Cbr>• tan(A ± B) = 1ttAan±~~ ~~tanA~~ ~~tanBB |\n| --- |\n| Double Angle Identities\u003Cbr>• cos 2A = cos2 A − sin2 A\u003Cbr>• cos 2A = 2 cos2 A − 1\u003Cbr>• cos 2A = 1 − 2 sin2 A\u003Cbr>• sin 2A = 2 cos AsinA\u003Cbr>• tan 2A =  2 tanA \u003Cbr>1 − tan2 A |\n| Half Angle Identities\u003Cbr>• cos A2 = ± r ~~ ~~1~~ ~~+~~ ~~c2os~~ ~~A\u003Cbr>• sin A2 = ± r ~~ ~~1~~ ~~−~~ ~~c2os~~ ~~AA 1 − cos A sinA\u003Cbr>• tan ~~ ~~ = ~~ ~~ = ~~  ~~2 sinA 1 + cos A |\n| Triple Angle Identities\u003Cbr>• cos 3A = 4 cos3 A − 3 cos A\u003Cbr>• sin 3A = 3 sinA − 4 sin3 A |\n| Power Reduction Identities\u003Cbr>• cos2 A = 1~~ ~~+~~ ~~co2s~~ ~~2A\u003Cbr>• sin2 A = 1~~ ~~−~~ ~~co2s~~ ~~2A\u003Cbr>• tan2 A = 11~~ ~~~~ ~~ccooss~~ ~~22AA • cos3 A = 3~~ ~~cos~~ ~~A~~ ~~+4~~ ~~cos~~ ~~3A\u003Cbr>• sin3 A = 3~~ ~~sinA~~ ~~−4~~ ~~sin~~ ~~3A |\n\nSum-to-Product Identities  \n• sinA + sin B = 2 sin 􀀒 A~~ ~~+2~~ ~~B 􀀓 cos 􀀒 A~~ ~~−2~~ ~~B 􀀓  \n• sinA − sin B = 2 cos 􀀒 A~~ ~~+2~~ ~~B 􀀓 sin 􀀒 A~~ ~~−2~~ ~~B 􀀓  \n• cos A + cos B = 2 cos 􀀒 A~~ ~~+2~~ ~~B 􀀓 cos 􀀒 A~~ ~~−2~~ ~~B 􀀓  \n• cos A − cos B = −2 sin 􀀒 A~~ ~~+2~~ ~~B 􀀓 sin 􀀒 A~~ ~~−2~~ ~~B 􀀓  \n\n| Product-to-Sum Identities\u003Cbr>• sinA cos B = 12 [sin(A + B) + sin(A − B)]\u003Cbr>• cos A cos B = 12 [cos(A + B) + cos(A − B)]\u003Cbr>• sinAsinB = 12 [cos(A − B) − cos(A + B)] |\n| --- |\n| Sums of Sines and Cosines\u003Cbr>• A cos x + B sinx = √A2 + B2 sin(x + φ) where cos φ = √A2B+~~ ~~B~~ ~~2 and sin φ = √A2A+~~ ~~B~~ ~~2\u003Cbr>• A cos x + B sinx = √A2 + B2 cos(x − φ) where\u003Cbr>\u003Cbr>cos φ = √A2A+~~ ~~B~~ ~~2 and sin φ = √A2B+~~ ~~B~~ ~~2 |\n| Laws of Sines and Cosines\u003Cbr>• c2 = a2 + b2 − 2ab cos C\u003Cbr> a   b   c \u003Cbr>• = =\u003Cbr>sinA sin B sin C |\n| Area of a Triangle\u003Cbr>For a triangle with sides a, b, c and angles 6 A, 6 B , and 6 C ,\u003Cbr>• Area = ps(s − a)(s − b)(s − c) where a + b + c\u003Cbr>s =\u003Cbr>2\u003Cbr>• Area = 12absin C\u003Cbr>• Area = c2~~ ~~si2nsA~~ ~~siin~~ ~~Cn~~ ~~B |\n| Circular Section\u003Cbr>• Arc length: s = rθ\u003Cbr>• Area: A = 12r2 θ |","cbCaitZSO8AEtBxe","https://ap.wps.com/l/cbCaitZSO8AEtBxe","pdf",749443,"English","# Factoring\n# Analytic Geometry\n# Exponent Rules\n# Logarithm Rules\n# Arithmetic Series\n# Geometric Series\n# Trigonometry\n## Trigonometric Identities","[{\"question\":\"What factoring identities are included in the reference sheet?\",\"answer\":\"It lists common products and squares such as a2 − b2 = (a − b)(a + b), and (a ± b)2 forms, plus sum/difference of cubes expansions for a3 + b3 and a3 − b3.\"},{\"question\":\"Which analytic geometry formulas are provided?\",\"answer\":\"The sheet includes slope m = (y2 − y1)/(x2 − x1), the point-slope form y − y1 = m(x − x1), and a distance formula d based on the coordinate differences.\"},{\"question\":\"What trigonometry identity categories are covered?\",\"answer\":\"It provides right-triangle ratio definitions (sin, cos, tan), Pythagorean identities, reciprocal and ratio identities, sum-and-difference identities, double-angle, half-angle, triple-angle, power-reduction, and product-to-sum forms.\"}]","Pre-Calculus Reference Sheet - Factoring & Analytic Geometry | PDF",1789900411]