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Additional coverage includes complex numbers, polar form, De Moivre’s theorem, rotation of axes, and key polar-coordinate conic sections (circles, parabolas, ellipses, hyperbolas) with focal and directrix details.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/algebra-and-trigonometry-james-stewart-fourth-edition/115165/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/algebra-and-trigonometry-james-stewart-fourth-edition/115165.png","ImageObject",300,407,{"name":42,"@type":43},"Jiven","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-23","2026-07-31",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",21,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is the quadratic formula and when is it used?","Question",{"text":63,"@type":64},"If ax^2 + bx + c = 0, then x = (-b ± √(b^2 - 4ac)) / (2a). It is used to solve quadratic equations for x.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Which absolute value properties are stated in the document?",{"text":68,"@type":64},"The document lists rules for comparing or transforming expressions involving a, b, and c, including cases with c > 0 or c \u003C 0 and how multiplication affects inequality directions. It also indicates how expressions like 0 \u003C x \u003C a translate into x = a or x = -2a in the provided cases.",{"name":70,"@type":61,"acceptedAnswer":71},"How are conic sections defined in polar or rotated-coordinate form?",{"text":72,"@type":64},"It presents rotation-of-axes formulas to eliminate xy-terms for general second-degree equations, then gives polar-coordinate descriptions such as circles and parabolas (x^2 = 4py) along with focus and directrix definitions. Ellipses and hyperbolas are given with focal parameters and standard polar relationships.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},115165,1785469631,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":96,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":140,"language":141,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":12,"update_tm":80,"read_time":145},962085662650,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","x mxn 5 xm1n  \n1 xm2n 5 x mn  \n1 xy2n 5 xnynx 1/n 5 !nx!n xy 5 !nx !ny  \n\"m !nx 5 \"n !mx 5 x  \nspecial products  \nxmxn 5 xm2nx 2n 5 x1n  \na xy~~ ~~ bn 5 xynn~~ ~~    xm/n 5 !nxm 5 1 !nx 2m Ån xy 5 !n!nxy  \n\n| 1 x 1 y 22 5 x2 1 2xy 1 y2\u003Cbr>1 x 2 y 22 5 x2 2 2xy 1 y2\u003Cbr>1 x 1 y 23 5 x 3 1 3x2y 1 3xy2 1 y 3\u003Cbr>1 x 2 y 23 5 x 3 2 3x2y 1 3xy2 2 y 3\u003Cbr>factoring formulas |\n| --- |\n| x2 2 y2 5 1 x 1 y 2 1 x 2 y 2 x2 1 2xy 1 y2 5 1 x 1 y 22\u003Cbr>x2 2 2xy 1 y2 5 1 x 2 y 22\u003Cbr>x 3 1 y 3 5 1 x 1 y 2 1 x2 2 xy 1 y22\u003Cbr>x 3 2 y 3 5 1 x 2 y 2 1 x2 1 xy 1 y22\u003Cbr>Quadratic formula |\n| If ax2 1 bx 1 c 5 0, then\u003Cbr>x 5\u003Cbr>2b 6 \"b2 2 4ac\u003Cbr>2a\u003Cbr>ineQualities and absolute value |\n\nIf a , b and b , c, then a , c.  \nIf a , b, then a 1 c , b 1 c.  \nIf a , b and c . 0, then ca , cb.  \nIf a , b and c , 0, then ca . cb. If a . 0, then  \n0 x 0 5 a means x 5 a or x 5 2a.  \n0 x 0 , a means 2a , x , a.  \n0 x 0 . a means x . a or x , 2a.  \nFormulas for area A, perimeter P, circumference C, volume V:  \nBox  \nV 5 l„h  \nl  \nPyramid  \nV 5 ~~13~~ ha2  \na  \nSphere  \nV 5 ~~43~~ pr3 A 5 4pr2  \nCone  \nV 5 ~~13~~ pr2h  \nheron’s formula  \nArea 5 !s1s 2 a 2 1s 2 b 2 1s 2 c 2  \nwhere s 5  \na 1 b 1 c 2  \nA  \nB  \nb  \nC  \nCopyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) . Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.  \nDistance between P11 x1 , y 12 and P21 x2 , y2 2 :  \nd 5 \"1x2 2 x122 1 1y2 2 y122 Midpoint of P1P2: ax1~~ ~~12~~ ~~x2~~ ~~ , y1~~ ~~12~~ ~~y2~~ ~~ b lines  \n\n| Slope of line through P11 x1 , y 1 2 and P21 x2 , y2 2\u003Cbr>Point-slope equation of line through P11 x1, y 12 with slope m Slope-intercept equation of line with slope m and y-intercept b Two-intercept equation of line with x-intercept a and y-intercept b\u003Cbr>logarithms |  | y2 2 y1 m 5 ~~  ~~x2 2 x1\u003Cbr>y 2 y 1 5 m 1 x 2 x12\u003Cbr>y 5 mx 1 b\u003Cbr>xa 1 yb 5 1 |\n| --- | --- | --- |\n| y 5 logax means ay 5 x loga ax 5 x\u003Cbr>loga 1 5 0\u003Cbr>log x 5 log 10 x\u003Cbr>loga xy 5 logax 1 logay\u003Cbr>logaxb 5 b logax | alogax 5 x loga a 5 1 ln x 5 logex\u003Cbr>logaax}y}b 5 logax 2 logay logb x 5 llooggaa~~ ~~xb |  |\n| exponential and logarithmic functions |  |  |\n\nLinear functions: f1x2 5 mx 1 b  \n\n| b |  |\n| --- | --- |\n|  |  |\n|  |  |\n\ny   \nx  \nÏ=b  \nPower functions: f1x2 5 xn  \nx  \nÏ=≈  \nRoot functions: f1x2 5 !nx  \nx  \nÏ=œ  \nx Ï=mx+b  \ny   \nÏ=x£  \nx  \nÏ=£œ  \nReciprocal functions: f1x2 5 1/xn  \ny   \nx  \nÏ=~~ ~~1x  \nAbsolute value function  \nx  \nÏ= | x |  \ny  \nx  \nÏ=  \nGreatest integer function  \nÏ=“x‘  \nCopyright 2016 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s) . Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.  \nFor the complex number z 5 a 1 bithe conjugate is z 5 a 2 bithe modulus is 0 z 0 5 \"a2 1 b2 the argument is u, where tan u 5 b/a  \nIm  \nbi  \na+bi  \n0 a Re  \nPolar form of a complex number  \nFor z 5 a 1 bi, the polar form is  \nz 5 r 1cos u 1 i sin u 2  \nwhere r 5 0 z 0 is the modulus of z and u is the argument of z  \nDe Moivre’s Theorem  \nzn 5 3r 1cos u 1 i sin u 2 4n 5 rn1 cos nu 1 i sin nu 2  \n!n z 5 3r 1cos u 1 i sin u 24 1/n  \n5 r1/na cos u~~ ~~1n2kp 1 i sin u~~ ~~1n2kpb where k 5 0, 1, 2, ... , n 2 1  \nrotation of axes  \nRotation of axes formulas  \nx 5 X cos f 2 Y sin fy 5 X sin f 1 Y cos f  \nAngle-of-rotation formula for conic sections To eliminate the xy-term in the equation  \nAx2 1 Bxy 1 Cy2 1 Dx 1 Ey 1 F 5 0 rotat","cbCaiirCGSirrJMO","https://ap.wps.com/l/cbCaiirCGSirrJMO","pdf",38474236,1175,"English","# Factoring and quadratic methods\n## Quadratic formula\n## Inequalities and absolute value\n# Geometry and analytic geometry\n## Distance and midpoint\n## Lines and slope forms\n## Area, perimeter, circumference, and volume\n# Functions\n## Linear, power, root, reciprocal\n## Absolute value and greatest integer\n## Exponential and logarithmic rules\n# Complex numbers and coordinate transformations\n## Modulus, argument, polar form\n## De Moivre’s theorem\n## Rotation of axes\n# Polar coordinates and conic sections\n## Circles\n## Parabolas\n## Ellipses\n## Hyperbolas","[{\"question\":\"What is the quadratic formula and when is it used?\",\"answer\":\"If ax^2 + bx + c = 0, then x = (-b ± √(b^2 - 4ac)) / (2a). It is used to solve quadratic equations for x.\"},{\"question\":\"Which absolute value properties are stated in the document?\",\"answer\":\"The document lists rules for comparing or transforming expressions involving a, b, and c, including cases with c \\u003e 0 or c \\u003c 0 and how multiplication affects inequality directions. It also indicates how expressions like 0 \\u003c x \\u003c a translate into x = a or x = -2a in the provided cases.\"},{\"question\":\"How are conic sections defined in polar or rotated-coordinate form?\",\"answer\":\"It presents rotation-of-axes formulas to eliminate xy-terms for general second-degree equations, then gives polar-coordinate descriptions such as circles and parabolas (x^2 = 4py) along with focus and directrix definitions. Ellipses and hyperbolas are given with focal parameters and standard polar relationships.\"}]","Algebra and Trigonometry - James Stewart - Fourth Edition | PDF",2961]