Talk:2070: Trig Identities - Revision history

172.70.85.221: Undo revision 290986 by Nayan123 (talk) Looks a lot like Spam (ill-formatted, at the very least).

2022-07-28T10:07:29Z

Undo revision 290986 by Nayan123 (talk) Looks a lot like Spam (ill-formatted, at the very least).

Nayan123: /* List of Essential Trigonometry formulas for Class 10, 11, and 12 */ new section

2022-07-28T10:00:23Z

‎List of Essential Trigonometry formulas for Class 10, 11, and 12: new section

Observer of the Absurd at 13:28, 15 May 2019

2019-05-15T13:28:15Z

Dgbrt: Please sign your comments.

2018-11-13T19:52:45Z

Please sign your comments.

162.158.123.91: reference to QBasic?

2018-11-13T05:23:14Z

reference to QBasic?

108.162.246.11: Maybe possibly Kingdom of Loathing reference?

2018-11-12T21:53:16Z

Maybe possibly Kingdom of Loathing reference?

Dgbrt: Please sign your comments.

2018-11-12T19:16:42Z

Please sign your comments.

Jimbob at 16:59, 12 November 2018

2018-11-12T16:59:28Z

162.158.79.149 at 16:58, 12 November 2018

2018-11-12T16:58:57Z

162.158.91.83 at 11:23, 12 November 2018

2018-11-12T11:23:50Z

← Older revision		Revision as of 10:07, 28 July 2022
Line 43:		Line 43:

	From when I saw <math> cin\theta </math> I knew the rest of the comic would be <math> \frac{b}{s}</math>. [[User:Observer of the Absurd\|Observer of the Absurd]] ([[User talk:Observer of the Absurd\|talk]]) 13:28, 15 May 2019 (UTC)		From when I saw <math> cin\theta </math> I knew the rest of the comic would be <math> \frac{b}{s}</math>. [[User:Observer of the Absurd\|Observer of the Absurd]] ([[User talk:Observer of the Absurd\|talk]]) 13:28, 15 May 2019 (UTC)
−
−	~~== List of Essential Trigonometry formulas for Class 10, 11, and 12 ==~~
−
−	~~Trigonometry formulas (source:https://inspiria.edu.in/trigonometry-formulas-for-class-12/)~~
−	If you are looking for the complete list of all trigonometry formulas for classes 10, 11, and 12, we have made it completely easy for you to understand and learn all trigonometry formulas and ratios to a single page. Memorizing these trigonometric formulas help students to solve trigonometry problems easily, which further leads to a good score in Mathematics. For easy understanding and access, we have provided the trigonometry table and inverse trigonometry formulas.
−	Trigonometry, a word derived from the Greek words ‘Trigon’ and ‘Metron’ refers to ‘measuring the sides of a triangle. This branch of mathematics studies the relation between angles and sides of triangles. Trigonometry formulas are used widely in various fields and have been in use since the 3rd Century BC. From Navigation to Celestial Mechanics to Engineering, Architecture and other various fields trigonometry play a vital role.
−	Various geometrical problems are solved using the trigonometry ratios Sine (Sin), Cosine (Cos), Tangent (Tan), Cotangent (cot), Secant (sec), and Cosecant (Csc), product identities, Pythagorean Identities, etc. There are several Trigonometric functions, formulas, and ratios like the sign of ratios in different quadrants, sum identities, difference identities, cofunction identities, double angle identities, half-angle identities, etc. These are introduced from Class 10th and the concept is further explained in classes 11th & 12th.
−	~~Trigonometry Formulas for Class 10, 11, and 12:~~
−	As trigonometry is the study of relationships between angles and sides of the triangles. The primary triangle studied is the right triangle. In a right-angled triangle, the three sides are named Hypotenuse, Opposite, and Adjacent. The longest side is called the Hypotenuse, the opposite side to the angle is called the Perpendicular (Opposite), and the side where both hypotenuse and opposite sits is the adjacent side.
−	~~Basic Formulas~~
−	~~Reciprocal Identities~~
−	~~Trigonometry Table~~
−	~~Periodic Identities~~
−	~~Co-function Identities~~
−	~~Sum and Difference Identities~~
−	~~Double Angle Identities~~
−	~~Triple Angle Identities~~
−	~~Half Angle Identities~~
−	~~Product Identities~~
−	~~Sum to Product Identities~~
−	~~Inverse Trigonometry Formulas~~
−
−	~~Basic Formulae~~
−	The basic Trigonometry formulas for class 10 are six basic ratios which are used for finding the elements in trigonometry which are called trigonometric functions. These are Sine (Sin), Cosine (Cos), Tangent (Tan), Cotangent (Cot), Secant (Sec), and Cosecant (Csc).
−	~~By taking right triangle as a reference, these Trigonometry functions are derived as following:~~
−	~~sin θ = Opposite Side/Hypotenuse~~
−	~~cos θ = Adjacent Side/Hypotenuse~~
−	~~tan θ = Opposite Side/Adjacent Side~~
−	~~sec θ = Hypotenuse/Adjacent Side~~
−	~~cosec θ = Hypotenuse/Opposite Side~~
−	~~cot θ = Adjacent Side/Opposite Side~~
−	~~Reciprocal Identities~~
−	~~Reciprocal identities are given as following:~~
−	~~cosec θ = 1/sin θ~~
−	~~sec θ = 1/cos θ~~
−	~~cot θ = 1/tan θ~~
−	~~sin θ = 1/cosec θ~~
−	~~cos θ = 1/sec θ~~
−	~~tan θ = 1/cot θ~~
−	These are taken from a right-angled triangle. As the height and base of the right triangle are given, we can find out the Sine (sin), Cosine (cos), Tangent (tan), Cotangent (cot), Secant (sec), and Cosecant (CSC) values using trigonometric formulas. These reciprocal trigonometric identities can also be derived by using the trigonometric functions.
−	~~Trigonometry Table~~
−	~~Below is the table for trigonometry formulas for angles that are commonly used for solving problems.~~
−	~~Angles (In Degrees)~~
−	0°
−	~~30°~~
−	~~45°~~
−	~~60°~~
−	~~90°~~
−	~~180°~~
−	~~270°~~
−	~~360°~~
−	~~Angles (In Radians)~~
−	0°
−	~~π/6~~
−	~~π/4~~
−	~~π/3~~
−	~~π/2~~
−	π
−	~~3π/2~~
−	2π
−	~~sin~~
−	0
−	~~1/2~~
−	~~1/√2~~
−	~~√3/2~~
−	1
−	0
−	-1
−	0
−	~~cos~~
−	1
−	~~√3/2~~
−	~~1/√2~~
−	~~1/2~~
−	0
−	-1
−	0
−	1
−	~~tan~~
−	0
−	~~1/√3~~
−	1
−	√3
−	∞
−	0
−	∞
−	0
−	~~cot~~
−	∞
−	√3
−	1
−	~~1/√3~~
−	0
−	∞
−	0
−	∞
−	~~csc~~
−	∞
−	2
−	√2
−	~~2/√3~~
−	1
−	∞
−	-1
−	∞
−	~~sec~~
−	1
−	~~2/√3~~
−	√2
−	2
−	∞
−	-1
−	∞
−	1
−
−	~~Periodicity Identities in Radian~~
−	After the basic formulas Trigonometry formula for Class 11 introduces periodicity Identities used in shifting the trigonometric functions by one period to the left or right. These are called co-function identities.
−	~~sin (π/2 – A) = cos A & cos (π/2 – A) = sin A~~
−	~~sin (π/2 + A) = cos A & cos (π/2 + A) = – sin A~~
−	~~sin (3π/2 – A) = – cos A & cos (3π/2 – A) = – sin A~~
−	~~sin (3π/2 + A) = – cos A & cos (3π/2 + A) = sin A~~
−	~~sin (π – A) = sin A & cos (π – A) = – cos A~~
−	~~sin (π + A) = – sin A & cos (π + A) = – cos A~~
−	~~sin (2π – A) = – sin A & cos (2π – A) = cos A~~
−	~~sin (2π + A) = sin A & cos (2π + A) = cos A~~
−	We know tall trigonometry functions in Class 11 are repetitive in nature, repeating themselves after this periodicity constant. This periodicity constant is different for different trigonometric identities. tan 45° = tan 225° but this is also true for cos 45° and cos 225°.
−	~~Co-function Identities (in Degrees~~
−	~~The co-function or periodic identities can also be represented in degrees as:~~
−	~~sin(90°−x) = cos x~~
−	~~cos(90°−x) = sin x~~
−	~~tan(90°−x) = cot x~~
−	~~cot(90°−x) = tan x~~
−	~~sec(90°−x) = csc x~~
−	~~csc(90°−x) = sec x~~
−	~~Sum & Difference Identities~~
−	~~sin(x+y) = sin(x)cos(y)+cos(x)sin(y)~~
−	~~cos(x+y) = cos(x)cos(y)–sin(x)sin(y)~~
−	~~tan(x+y) = (tan x + tan y)/ (1−tan x •tan y)~~
−	~~sin(x–y) = sin(x)cos(y)–cos(x)sin(y)~~
−	~~cos(x–y) = cos(x)cos(y) + sin(x)sin(y)~~
−	~~tan(x−y) = (tan x–tan y)/ (1+tan x • tan y)~~
−	~~Double Angle Identities~~
−	~~sin(2x) = 2sin(x) • cos(x) = [2tan x/(1+tan2 x)]~~
−	~~cos(2x) = cos2(x)–sin2(x) = [(1-tan2 x)/(1+tan2 x)]~~
−	~~cos(2x) = 2cos2(x)−1 = 1–2sin2(x)~~
−	~~tan(2x) = [2tan(x)]/ [1−tan2(x)]~~
−	~~sec (2x) = sec2 x/(2-sec2 x)~~
−	~~csc (2x) = (sec x. csc x)/2~~
−	~~Triple Angle Identities~~
−	~~Sin 3x = 3sin x – 4sin3x~~
−	~~Cos 3x = 4cos3x-3cos x~~
−	~~Tan 3x = [3tanx-tan3x]/[1-3tan2x]~~

← Older revision		Revision as of 10:00, 28 July 2022
Line 43:		Line 43:

	From when I saw <math> cin\theta </math> I knew the rest of the comic would be <math> \frac{b}{s}</math>. [[User:Observer of the Absurd\|Observer of the Absurd]] ([[User talk:Observer of the Absurd\|talk]]) 13:28, 15 May 2019 (UTC)		From when I saw <math> cin\theta </math> I knew the rest of the comic would be <math> \frac{b}{s}</math>. [[User:Observer of the Absurd\|Observer of the Absurd]] ([[User talk:Observer of the Absurd\|talk]]) 13:28, 15 May 2019 (UTC)
		+
		+	== List of Essential Trigonometry formulas for Class 10, 11, and 12 ==
		+
		+	Trigonometry formulas (source:https://inspiria.edu.in/trigonometry-formulas-for-class-12/)
		+	If you are looking for the complete list of all trigonometry formulas for classes 10, 11, and 12, we have made it completely easy for you to understand and learn all trigonometry formulas and ratios to a single page. Memorizing these trigonometric formulas help students to solve trigonometry problems easily, which further leads to a good score in Mathematics. For easy understanding and access, we have provided the trigonometry table and inverse trigonometry formulas.
		+	Trigonometry, a word derived from the Greek words ‘Trigon’ and ‘Metron’ refers to ‘measuring the sides of a triangle. This branch of mathematics studies the relation between angles and sides of triangles. Trigonometry formulas are used widely in various fields and have been in use since the 3rd Century BC. From Navigation to Celestial Mechanics to Engineering, Architecture and other various fields trigonometry play a vital role.
		+	Various geometrical problems are solved using the trigonometry ratios Sine (Sin), Cosine (Cos), Tangent (Tan), Cotangent (cot), Secant (sec), and Cosecant (Csc), product identities, Pythagorean Identities, etc. There are several Trigonometric functions, formulas, and ratios like the sign of ratios in different quadrants, sum identities, difference identities, cofunction identities, double angle identities, half-angle identities, etc. These are introduced from Class 10th and the concept is further explained in classes 11th & 12th.
		+	Trigonometry Formulas for Class 10, 11, and 12:
		+	As trigonometry is the study of relationships between angles and sides of the triangles. The primary triangle studied is the right triangle. In a right-angled triangle, the three sides are named Hypotenuse, Opposite, and Adjacent. The longest side is called the Hypotenuse, the opposite side to the angle is called the Perpendicular (Opposite), and the side where both hypotenuse and opposite sits is the adjacent side.
		+	Basic Formulas
		+	Reciprocal Identities
		+	Trigonometry Table
		+	Periodic Identities
		+	Co-function Identities
		+	Sum and Difference Identities
		+	Double Angle Identities
		+	Triple Angle Identities
		+	Half Angle Identities
		+	Product Identities
		+	Sum to Product Identities
		+	Inverse Trigonometry Formulas
		+
		+	Basic Formulae
		+	The basic Trigonometry formulas for class 10 are six basic ratios which are used for finding the elements in trigonometry which are called trigonometric functions. These are Sine (Sin), Cosine (Cos), Tangent (Tan), Cotangent (Cot), Secant (Sec), and Cosecant (Csc).
		+	By taking right triangle as a reference, these Trigonometry functions are derived as following:
		+	sin θ = Opposite Side/Hypotenuse
		+	cos θ = Adjacent Side/Hypotenuse
		+	tan θ = Opposite Side/Adjacent Side
		+	sec θ = Hypotenuse/Adjacent Side
		+	cosec θ = Hypotenuse/Opposite Side
		+	cot θ = Adjacent Side/Opposite Side
		+	Reciprocal Identities
		+	Reciprocal identities are given as following:
		+	cosec θ = 1/sin θ
		+	sec θ = 1/cos θ
		+	cot θ = 1/tan θ
		+	sin θ = 1/cosec θ
		+	cos θ = 1/sec θ
		+	tan θ = 1/cot θ
		+	These are taken from a right-angled triangle. As the height and base of the right triangle are given, we can find out the Sine (sin), Cosine (cos), Tangent (tan), Cotangent (cot), Secant (sec), and Cosecant (CSC) values using trigonometric formulas. These reciprocal trigonometric identities can also be derived by using the trigonometric functions.
		+	Trigonometry Table
		+	Below is the table for trigonometry formulas for angles that are commonly used for solving problems.
		+	Angles (In Degrees)
		+	0°
		+	30°
		+	45°
		+	60°
		+	90°
		+	180°
		+	270°
		+	360°
		+	Angles (In Radians)
		+	0°
		+	π/6
		+	π/4
		+	π/3
		+	π/2
		+	π
		+	3π/2
		+	2π
		+	sin
		+	0
		+	1/2
		+	1/√2
		+	√3/2
		+	1
		+	0
		+	-1
		+	0
		+	cos
		+	1
		+	√3/2
		+	1/√2
		+	1/2
		+	0
		+	-1
		+	0
		+	1
		+	tan
		+	0
		+	1/√3
		+	1
		+	√3
		+	∞
		+	0
		+	∞
		+	0
		+	cot
		+	∞
		+	√3
		+	1
		+	1/√3
		+	0
		+	∞
		+	0
		+	∞
		+	csc
		+	∞
		+	2
		+	√2
		+	2/√3
		+	1
		+	∞
		+	-1
		+	∞
		+	sec
		+	1
		+	2/√3
		+	√2
		+	2
		+	∞
		+	-1
		+	∞
		+	1
		+
		+	Periodicity Identities in Radian
		+	After the basic formulas Trigonometry formula for Class 11 introduces periodicity Identities used in shifting the trigonometric functions by one period to the left or right. These are called co-function identities.
		+	sin (π/2 – A) = cos A & cos (π/2 – A) = sin A
		+	sin (π/2 + A) = cos A & cos (π/2 + A) = – sin A
		+	sin (3π/2 – A) = – cos A & cos (3π/2 – A) = – sin A
		+	sin (3π/2 + A) = – cos A & cos (3π/2 + A) = sin A
		+	sin (π – A) = sin A & cos (π – A) = – cos A
		+	sin (π + A) = – sin A & cos (π + A) = – cos A
		+	sin (2π – A) = – sin A & cos (2π – A) = cos A
		+	sin (2π + A) = sin A & cos (2π + A) = cos A
		+	We know tall trigonometry functions in Class 11 are repetitive in nature, repeating themselves after this periodicity constant. This periodicity constant is different for different trigonometric identities. tan 45° = tan 225° but this is also true for cos 45° and cos 225°.
		+	Co-function Identities (in Degrees
		+	The co-function or periodic identities can also be represented in degrees as:
		+	sin(90°−x) = cos x
		+	cos(90°−x) = sin x
		+	tan(90°−x) = cot x
		+	cot(90°−x) = tan x
		+	sec(90°−x) = csc x
		+	csc(90°−x) = sec x
		+	Sum & Difference Identities
		+	sin(x+y) = sin(x)cos(y)+cos(x)sin(y)
		+	cos(x+y) = cos(x)cos(y)–sin(x)sin(y)
		+	tan(x+y) = (tan x + tan y)/ (1−tan x •tan y)
		+	sin(x–y) = sin(x)cos(y)–cos(x)sin(y)
		+	cos(x–y) = cos(x)cos(y) + sin(x)sin(y)
		+	tan(x−y) = (tan x–tan y)/ (1+tan x • tan y)
		+	Double Angle Identities
		+	sin(2x) = 2sin(x) • cos(x) = [2tan x/(1+tan2 x)]
		+	cos(2x) = cos2(x)–sin2(x) = [(1-tan2 x)/(1+tan2 x)]
		+	cos(2x) = 2cos2(x)−1 = 1–2sin2(x)
		+	tan(2x) = [2tan(x)]/ [1−tan2(x)]
		+	sec (2x) = sec2 x/(2-sec2 x)
		+	csc (2x) = (sec x. csc x)/2
		+	Triple Angle Identities
		+	Sin 3x = 3sin x – 4sin3x
		+	Cos 3x = 4cos3x-3cos x
		+	Tan 3x = [3tanx-tan3x]/[1-3tan2x]

← Older revision		Revision as of 13:28, 15 May 2019
Line 41:		Line 41:

	I thought "distance 2 banana" had to be a reference to QBasic's Gorillas game. "Enchant at target" could refer to the banana exploding when it hits something. mrpsbrk {{unsigned ip\|162.158.123.91}}		I thought "distance 2 banana" had to be a reference to QBasic's Gorillas game. "Enchant at target" could refer to the banana exploding when it hits something. mrpsbrk {{unsigned ip\|162.158.123.91}}
		+
		+	From when I saw <math> cin\theta </math> I knew the rest of the comic would be <math> \frac{b}{s}</math>. [[User:Observer of the Absurd\|Observer of the Absurd]] ([[User talk:Observer of the Absurd\|talk]]) 13:28, 15 May 2019 (UTC)

← Older revision		Revision as of 19:52, 13 November 2018
Line 40:		Line 40:
	<math>\frac{d}{dx}\sec x=\sec x\tan x=</math> sex tanks. [[User:Probably not Douglas Hofstadter\|Probably not Douglas Hofstadter]] ([[User talk:Probably not Douglas Hofstadter\|talk]]) 21:36, 11 November 2018 (UTC)		<math>\frac{d}{dx}\sec x=\sec x\tan x=</math> sex tanks. [[User:Probably not Douglas Hofstadter\|Probably not Douglas Hofstadter]] ([[User talk:Probably not Douglas Hofstadter\|talk]]) 21:36, 11 November 2018 (UTC)

−	I thought "distance 2 banana" had to be a reference to QBasic's Gorillas game. "Enchant at target" could refer to the banana exploding when it hits something. mrpsbrk	+	I thought "distance 2 banana" had to be a reference to QBasic's Gorillas game. "Enchant at target" could refer to the banana exploding when it hits something. mrpsbrk {{unsigned ip\|162.158.123.91}}

← Older revision		Revision as of 05:23, 13 November 2018
Line 39:		Line 39:

	<math>\frac{d}{dx}\sec x=\sec x\tan x=</math> sex tanks. [[User:Probably not Douglas Hofstadter\|Probably not Douglas Hofstadter]] ([[User talk:Probably not Douglas Hofstadter\|talk]]) 21:36, 11 November 2018 (UTC)		<math>\frac{d}{dx}\sec x=\sec x\tan x=</math> sex tanks. [[User:Probably not Douglas Hofstadter\|Probably not Douglas Hofstadter]] ([[User talk:Probably not Douglas Hofstadter\|talk]]) 21:36, 11 November 2018 (UTC)
		+
		+	I thought "distance 2 banana" had to be a reference to QBasic's Gorillas game. "Enchant at target" could refer to the banana exploding when it hits something. mrpsbrk

@@ Line 17: / Line 17: @@
 :I think it is a Magic: The Gathering reference. Although it is phrased oddly. You'd think it would be "at target enchantment", rather than "target at enchantment". --[[User:Dryhamm|Dryhamm]] ([[User talk:Dryhamm|talk]]) 21:04, 9 November 2018 (UTC)
 :: Likely, it refers to the bigbox retailer, Target. {{unsigned ip|172.68.58.233}}
 :Voila - s=t. {{unsigned|Elliott}}

@@ Line 9: / Line 9: @@
 ::cas is realtively easy... it is cos(theta)=a/c -> cs(theta)=ao/c -> cas(theta)=o/c; when you realise that the top one isn't zero but o it clicks [[Special:Contributions/141.101.96.209|141.101.96.209]] 23:35, 9 November 2018 (UTC)
 :::You made the same error Randall did: you divided by 'o' on the left and multiplied on the right.  I think the theme of the page is expanding significantly upon common math errors that were already humorous, like the common proof of 5=3 by dividing and multiplying by zero.  The error here is in line with the theme of casual beginner errors. [[Special:Contributions/172.68.51.154|172.68.51.154]]
-:: You can see cin is derived from sin by swapping the positions of c and s. Likewise, Switching the a and o in cos(theta) = a/c gives cas(theta) = o/c i.e. no need for multiplicative consistency. The rule of treating things as a product of terms is implemented fully in the following lines.
+:: You can see cin is derived from sin by swapping the positions of c and s. Likewise, Switching the a and o in cos(theta) = a/c gives cas(theta) = o/c i.e. no need for multiplicative consistency. The rule of treating things as a product of terms is implemented fully in the following lines. [[Special:Contributions/162.158.91.83|162.158.91.83]] 11:23, 12 November 2018 (UTC)
 ::: <math> sin \theta = b/c</math> leading to <math>cin \theta = b/s</math> is algebraically valid if you interpret sin as the product of s, i, n by multiplying both sides by c/s.  It is not valid to just "swap" two letters in one equation that is part of a system of equations.  You could do the same trick and get <math>cas \theta = a^2/oc</math> from <math>cos \theta = a/c</math> or start with <math>sec \theta = c/a</math> and get <math>cas \theta = c/e</math>.  Note for all equations except <math>cas \theta = o/c</math> and switching an <math>s</math> to a <math>t</math> to find <math>tan \theta = insect \theta^2</math>, the equations can be correctly derived by treating trig functions as product of single letter variables and algebraically manipulating them. [[User:Jimbob|Jimbob]] ([[User talk:Jimbob|talk]]) 16:59, 12 November 2018 (UTC)
@@ Line 16: / Line 16: @@
 Is Enchant at target a magic:the gathering reference? [[User:AncientSwordRage|AncientSwordRage]] ([[User talk:AncientSwordRage|talk]]) 20:55, 9 November 2018 (UTC)
 :I think it is a Magic: The Gathering reference. Although it is phrased oddly. You'd think it would be "at target enchantment", rather than "target at enchantment". --[[User:Dryhamm|Dryhamm]] ([[User talk:Dryhamm|talk]]) 21:04, 9 November 2018 (UTC)
-:: Likely, it refers to the bigbox retailer, Target.
+:: Likely, it refers to the bigbox retailer, Target. {{unsigned ip|172.68.58.233}}
-:Voila - s=t.
+:Voila - s=t. {{unsigned|Elliott}}
 ::That was incredible! (assuming previous poster discovered the extrapolated proof in the description) [[Special:Contributions/172.68.51.154|172.68.51.154]] 01:47, 10 November 2018 (UTC)
-::Combining <math>\cos\theta=\frac{a}{c}</math> and <math>\mathrm{cas}\ \theta=\frac{o}{c}</math> allows you to conclude <math>a^2 = o^2</math>, not <math>a=o</math>.
+::Combining <math>\cos\theta=\frac{a}{c}</math> and <math>\mathrm{cas}\ \theta=\frac{o}{c}</math> allows you to conclude <math>a^2 = o^2</math>, not <math>a=o</math>. {{unsigned ip|162.158.146.10}}
 Somebody added a comment on puns, e.g. that "cin sucks".  More explanation is needed.  It looks like some kind of a meta-joke.  If you ask why, and start interpreting, you see that "b/c" == "because".  It might be the answer to why the puns line should be removed, though.  [[Special:Contributions/172.68.51.154|172.68.51.154]]
-For the Bot->Boat->Stoat line, this comes from the word game where you add/change letters to make a new word. Start with bot=a/c, multiply by a on both sides gets boat=a^2/c. Multiply by st on both sides and divide b on both sides gets Stoat=a^2/c*St/b.
+For the Bot->Boat->Stoat line, this comes from the word game where you add/change letters to make a new word. Start with bot=a/c, multiply by a on both sides gets boat=a^2/c. Multiply by st on both sides and divide b on both sides gets Stoat=a^2/c*St/b. {{unsigned ip|162.158.78.166}}
 Uh... people... THE NAME GAME? Hello?
-https://en.wikipedia.org/wiki/The_Name_Game
+https://en.wikipedia.org/wiki/The_Name_Game {{unsigned ip|162.158.79.107}}
 Checking through the math, just working from the real trig identities, without considering Randall's at-first-glance questionable identities like cas theta = o/c, basically everything that does not have a factor of d or 2 in it is equal to 1, and d is equal to 1/2, which then establishes the more questionable identities as tautological, 1=1. [[Special:Contributions/162.158.142.100|162.158.142.100]] 04:09, 10 November 2018 (UTC)
@@ Line 35: / Line 35: @@
 Am I the only one who saw  t²n²a⁴ as "tuna"?  [[Special:Contributions/172.68.58.233|172.68.58.233]] 14:17, 10 November 2018 (UTC)
-:Yes.
+:Yes. {{unsigned ip|162.158.75.190}}
 <math>\frac{d}{dx}\sec x=\sec x\tan x=</math> sex tanks. [[User:Probably not Douglas Hofstadter|Probably not Douglas Hofstadter]] ([[User talk:Probably not Douglas Hofstadter|talk]]) 21:36, 11 November 2018 (UTC)