Talk:2070: Trig Identities

2018-11-10T00:16:24Z

Elliott:

I am confused by the insect line. This seems to be true only if s=t.
[[Special:Contributions/141.101.96.209|141.101.96.209]] 19:03, 9 November 2018 (UTC)

:That one and the `cas` aren't making any sense to me. [[User:GreatBigDot|GreatBigDot]] ([[User talk:GreatBigDot|talk]]) 20:02, 9 November 2018 (UTC)
::Oh, the casinus is much important to... What was it? --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 20:15, 9 November 2018 (UTC)
::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)

:I think insect is.. a bug.. ;) [[User:Smerriman|Smerriman]] ([[User talk:Smerriman|talk]]) 20:18, 9 November 2018 (UTC)

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)

:Voila - s=t.

2070: Trig Identities

2018-11-10T00:14:13Z

Elliott: "Proof" that "s" ="t"

{{comic
| number = 2070
| date = November 9, 2018
| title = Trig Identities
| image = trig_identities.png
| titletext = ARCTANGENT THETA = ENCHANT AT TARGET
}}

==Explanation==
{{incomplete|Please only mention here why this explanation isn't complete. Do NOT delete this tag too soon.}}
This comic shows several real and fictitious {{w|List_of_trigonometric_identities#Trigonometric_functions|trigonometric identities}}. Most of the identities past the second line are "derived" by applying algebraic methods to the letters in the trig functions, which violates the rules of math, since the trig functions are operators and not variables.

The first line are well known trigonometric functions. The second line contains the lesser known reciprocals of the trigonometric functions in the first line.

The following identities are made up and are increasing in absurdity. The comic reflects on the confusion one gets when working more intensely with these identities, since there are a lot of hidden dependencies between them.

The third and fourth line is made by treating the trigonometric function as a product of variables rather than a function and then using the above identities to create words. e.g. sin = b/c -> cin = b/s (this could also be a reference to the C++ cin).

The second to last line performs some algebra on the individual letters of <math>(\mathrm{tan}\ \theta)^2=\frac{b^2}{a^2}</math> as a setup to the last line. The last line takes the formula <math>distance=\frac{1}{2}at^2</math> "from physics" and plugs it into the equation of the previous line, doing some algebra to replace <math>at^2</math> with <math>distance2</math> and expanding <math>(na)^2</math> into <math>nana</math> to get the final equation, <math>distance2banana=\frac{b^3}{\theta^2}</math> . Using the rules already established in this comic, this is valid algebra. The distance equation is the distance a constantly accelerating object initially at rest moves in a given length of time t, most often used to find how far an object dropped from rest will fall under the influence of gravity in a given amount of time (or how long it will take to fall a given distance).

There seem to be (at least) two errors in the formulars:
* <math>\mathrm{cas}\ \theta=\frac{o}{c}</math> seems to be derived from <math>\cos\theta=\frac{a}{c}</math> but to reach "cas" from "cos" one has to divide by "o" and multiply by "a". This would lead to <math>\frac{a^2}{co}</math> on the right hand side.
* In the identity <math>\sin\theta\sec\theta=\mathrm{insect}\theta^2</math> one of the "s"'s has turned into a "t". This can be found by combining <math>\cos\theta=\frac{a}{c}</math>, <math>\mathrm{cas}\ \theta=\frac{o}{c}</math>, which show <math>o=a</math>, and <math>s=\frac{1}{c^2\theta}</math>. Using this with <math>\csc\theta=\frac{c}{b}</math> you can "prove" <math>c=b</math> and then with with <math>\cot\theta=\frac{a}{b}</math> you can find <math>t=\frac{1}{c^2\theta}=s</math>.

The title-text is an anagram. Due to the commutative property of multiplication (which states that order does not affect the product), these equations are equivalent if treated as individual variables as earlier. Another layer of absurdity is added in that the variable Theta is spelled out and broken into its letters, which are then treated as individual variables. (The {{w|arctangent}} referred to here is the inverse tangent, a one-sided inverse to the tangent function. You would not normally write <math>\arctan\theta</math>, since the theta in the comic refers to an angle, and the arctangent has an angle as its ''value'' rather than as its ''argument''; however, using theta here is merely unconventional, not forbidden.)

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:[Inside a single frame comic a right-angled triangle is shown. The short edges are labeled "a" and "b" respectively and the long edge has a "c". All angles are marked, the right angle by a square and the both others by an arc. One arc is labeled by the Greek symbol theta.]

:[Trigonometric functions on the marked angle theta in relation to "a", "b", and many more not depicted other variables are shown:]

:[Caption below the frame:]
:Key trigonometric identities

{{comic discussion}}

[[Category:Math]]

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Talk:2070: Trig Identities

2070: Trig Identities