[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-572874-105":53,"doc-detail-572874-en":126},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":119,"head_meta":121,"extra_data":123,"updated_unix":125},105,"en","calc-ii-cheat-sheets-fundamental-identities-trigonometry-and-calculus-formulas","Calc II Cheat Sheets - Fundamental Identities - Trigonometry and Calculus Formulas","","Compact reference sheet for Calc II covering angle measurement in radians, right-angle trigonometry, trigonometric and inverse trigonometric functions, plus graphs of standard trig functions. Includes a table of key angles with sine, cosine, and tangent values, and lists fundamental identities (Pythagorean, reciprocal, even/odd). Adds law of sines and cosines, addition/subtraction, double- and half-angle formulas, and hyperbolic/inverse hyperbolic function definitions. Also provides geometric formulas, factoring identities, and numerical integration rules such as midpoint, trapezoidal, and Simpson’s rule with applications to lengths and areas.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":46,"@type":70,"position":76},"https://docshare.wps.com/template/paper-templates/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/calc-ii-cheat-sheets-fundamental-identities-trigonometry-and-calculus-formulas/572874/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/calc-ii-cheat-sheets-fundamental-identities-trigonometry-and-calculus-formulas/572874.png","ImageObject",442,249,{"name":88,"@type":89},"Liam","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-15","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":9},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What conversion relates radians and degrees for angle measurement?","Question",{"text":108,"@type":109},"Use π radians = 180°.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"Which fundamental identity connects sine and cosine?",{"text":113,"@type":109},"sin²θ + cos²θ = 1.",{"name":115,"@type":106,"acceptedAnswer":116},"How are numerical integration errors approximated in common rules?",{"text":117,"@type":109},"The sheet states error bounds in terms of |f''(x)| and |f''''(x)| for midpoint, trapezoidal, and Simpson’s rules on a≤x≤b, and then gives the midpoint, trapezoidal, and Simpson approximations.","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},572874,1792052381,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":45,"category_name":46,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":9,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":135,"language":136,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":61,"update_tm":140,"read_time":73},8796095461564,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Angle Measurement  \nπ radians=180°  \ns=rθ  \n(θ in radians)  \nRight Angle Trigonometry  \nTrigonometric Functions  \nGraphs of Trigonometric Functions  \nTrigonometric Functions of Important Angles  \n\n| θ   | radians   | sin θ   | cosθ   | tan θ   |\n| --- | --- | --- | --- | --- |\n| 0°   | 0   | 0   | 1   | 0   |\n| 30°   | π/6   | 1/2   | √3/2   | √3/3   |\n| 45°   | π/4   | √2/2   | √2/2   | 1   |\n| 60°   | π/3   | √3/2   | 1/2   | √3   |\n| 90°   | π/2   | 1   | 0   | 一   |\n\nInverse Trigonometric Functions  \narcsinx=sin⁻¹x=y⇔siny=x andarccosx=cos⁻¹x=y台cosy=x and 0≤y≤π  \nCalc II Cheat Sheets  \nFundamental ldentities  \nsin²θ+cos²θ=1  \n1+tan²θ=sec²θ  \n1+cot²θ=csc²θ  \nsin(-θ)=-sin θ  \ncos(-θ)=cosθ  \ntan(-θ)=-tan θ  \nThe Law of Sines  \nThe Law of Cosines  \na²=b²+c²-2bc cos A  \nb²=a²+c²-2ac cos B  \nc²=a²+b²-2ab cos C  \nAddition and Subtraction Formulas  \nsin(x+y)=sinx cos y+cosx sin ysin(x-y)=sin x cosy-cosx sin ycos(x+y)=cosx cosy-sinx sin ycos(x-y)=cosx cosy+sin x sin y  \nDouble-Angle Formulas  \nsin 2x=2sinx cos xcos 2x=cos²x-sin²x=2 cos²x-1=1-2 sin²x  \nHalf-Angle Formulas  \ny=tan⁻¹x=arctan x  \nHyperbolic Functions  \nInverse Hyperbolic Functions  \ny=sinh⁻¹x      sinhy=x  \ny=cosh-¹x⇔cosh y=x and y≥0y=tanh⁻¹x⇔  tanh y=x  \nArithmetic Operations  \na(b+c)=ab+ac  \nExponents and Radicals  \nx\"x\"=x+\\#  \n(x\")\"=x\"\"  \n(xy)\"=x\"y\"  \nx/n=“x  \nx\"/n=√x\"=(Vx)”  \n\"xy =Vxy  \nFactoring Special Polynomials  \nx²-y²=(x+y)(x-y)  \nx³+y³=(x+y)(x²-xy+y²)  \nx³-y³=(x-y)(x²+xy+y²)  \n# Calc II Cheat Sheets\n\nsinh⁻¹x=1n(x+√x²+1)cosh⁻¹x=1n(x+√x²-1)  \nGeometric Formulas  \nFormulas for area A,circumference C,and volume V:  \nTriangle  \nCircle  \nSector of Circle  \nA=πr²  \nA=bh  \nA=r²θ  \n=÷ab sinθ  \ns=rθ(θ in radians)  \nC=2πr  \nSphere  \nV=专πr³  \nV=πr²h  \nA=4πr²  \nCylinder  \nV=πr²h  \nCone  \nA=πr√r²+h²  \nCalc II Cheat Sheets  \nGeneral Formulas  \nL  \n5.  \n)(Product Rule)  \n8.  \nExponential and Logarithmic Functions  \n9.  \n10.  \n11.  \nTrigonometric Functions  \n14.  \nInverse Trigonometric Functions  \nHyperbolic Functions  \nInverse Hyperbolic Functions  \n(Quotient I  \n(Power Rule)  \nCalc II Cheat Sheets  \n## Basic Forms\n\n11.  \n2.  \n,n≠-1  \n12.  \n13.  \n14.  \n15.  \n,a>0  \n16.  \n17.  \n18.  \n19.  \n20.  \n10.  \nForms Involving√a²+u²,a>0  \n21.  \n23.  \n25.  \nCalc II Cheat Sheets  \nMidpoint Rule:  \nSuppose |f\"(x)|≤K and|f(⁴(x)|≤L for a≤x≤b.Theerrors in the Midpoint,Trapezoidal,and Simpson's Rules aregiven by,respectively,  \nI≈M=△x[f(x₁)+f(x₂)+…+f(xn)]  \nwhere x;is the midpoint of [xi-1,x;].  \nTrapezoidal Rule:  \nI≈Tn  \nSimpson's Rule:  \nI≈S,+2f(xn-2)+4f(xn-1)+f(xn)]  \nwhere n is even.  \nWrite an expression for the length of a smooth curvegiven by y=f(x),a≤x≤b.  \nWhat if x is given as a function of y?  \nWrite an expression for the surface area of the surfaceobtained by rotating the curve y=f(x),a≤x≤b,aboutthe x-axis.  \nWhat if x is given as a function of y?  \nWhat if the curve is rotated about the y-axis?  \nor  \nHow do you find the slope of a tangent line to a polarcurve?  \nHow do you find the slope of a tangent to a parametriccurve?  \nYou can find dy/dx as a function of t by calculating  \nif dx/dt≠0  \nHow do you find the area under a parametric curve?  \nIf the curve is traced out once by the parametric equationsx=f(t),y=g(t),α≤t≤β,then the area is  \n[or jβg(1f'(t)dt if the leftmost point is(f(β),g(β))rather than(f(a),g(α))].  \nite an expression for each of the following:  \nThe length of a parametric curve  \nIf the curve is traced out once by the parametric equationsx=f(t),y=g(t),α≤t≤β,then the length is  \nThe area of the surface obtained by rotating a parametriccurve about the x-axis  \nHow do you find the area of a region bounded by a polarcurve?  \nHow do you find the length of a polar curve?  \nCalc II Cheat Sheets  \n6Geon'c senu:·RatioTest:a一bu+ la./div.,Def:ais (mlitiomuly umZ la.lis lenvis absolukely Comv ,if二R≤Hhrc人 o≤ bu+I≤bn cn6。→0·Est.f 5= 2(-⁻bn,ALt.Series Test:→0 f m≤外,比,thu(6If大a=(-1)”“b.尺。≤ ,thonaccord2ingly.inden o2a工au&℃=th se     \n,Thm:If a→Con  7 a、→0  \n3.Jf Lik abovt,Thm:f","cbCaimqghejfYdju","https://ap.wps.com/l/cbCaimqghejfYdju","pdf",2667938,6,"English","# Angle Measurement and Trigonometry\n## Right Angle Trigonometry and Key Functions\n## Inverse Trigonometric Functions\n## Fundamental Identities and Laws\n# Formulas for Trigonometric Manipulation\n## Addition, Subtraction, Double-Angle, Half-Angle\n# Hyperbolic and Inverse Hyperbolic Functions\n# Algebraic and Factoring Identities\n# Geometric Formulas\n## Area, Circumference, Sector, Sphere and Volume\n# Integration Rules and Applications\n## Midpoint, Trapezoidal, and Simpson’s Rule\n## Length and Surface Area by Rotation\n## Parametric and Polar Curve Slope and Area","[{\"question\":\"What conversion relates radians and degrees for angle measurement?\",\"answer\":\"Use π radians = 180°.\"},{\"question\":\"Which fundamental identity connects sine and cosine?\",\"answer\":\"sin²θ + cos²θ = 1.\"},{\"question\":\"How are numerical integration errors approximated in common rules?\",\"answer\":\"The sheet states error bounds in terms of |f''(x)| and |f''''(x)| for midpoint, trapezoidal, and Simpson’s rules on a≤x≤b, and then gives the midpoint, trapezoidal, and Simpson approximations.\"}]","Calc II Cheat Sheets - Fundamental Identities - Trigonometry and Calculus Formulas | PDF",1791929809]