Difference between revisions of "Talk:2070: Trig Identities"
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I am confused by the insect line. This seems to be true only if s=t. | 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) | [[Special:Contributions/141.101.96.209|141.101.96.209]] 19:03, 9 November 2018 (UTC) | ||
+ | :I added a note regarding how similar it sounds to 'sinsec'. [[Special:Contributions/172.68.51.154|172.68.51.154]] 01:47, 10 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) | :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) | ::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) | ||
+ | :::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. [[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) | ||
:I think insect is.. a bug.. ;) [[User:Smerriman|Smerriman]] ([[User talk:Smerriman|talk]]) 20:18, 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) | ||
+ | :: Likely, it refers to the bigbox retailer, Target. {{unsigned ip|172.68.58.233}} | ||
+ | ::: To me it sounds more like a reference to a [https://www.kingdomofloathing.com/ nerdy video game], where a [http://kol.coldfront.net/thekolwiki/index.php/Wand_of_Nagamar certain object] worked like this, turning e.g. '''BEAM OF DARK ENERGY''' into a '''BAKED FERRY GNOME''' [[Special:Contributions/108.162.246.11|108.162.246.11]] 21:53, 12 November 2018 (UTC) | ||
+ | |||
+ | :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>. {{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. {{unsigned ip|162.158.78.166}} | ||
+ | |||
+ | Uh... people... THE NAME GAME? Hello? | ||
+ | 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) | ||
+ | |||
+ | |||
+ | <math>\sec\theta = sect \eta</math> [[Special:Contributions/141.101.104.71|141.101.104.71]] 13:36, 10 November 2018 (UTC) AndreasH | ||
+ | |||
+ | 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. {{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) | ||
+ | |||
+ | 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) |
Latest revision as of 10:07, 28 July 2022
I am confused by the insect line. This seems to be true only if s=t.
141.101.96.209 19:03, 9 November 2018 (UTC)
- I added a note regarding how similar it sounds to 'sinsec'. 172.68.51.154 01:47, 10 November 2018 (UTC)
- That one and the `cas` aren't making any sense to me. GreatBigDot (talk) 20:02, 9 November 2018 (UTC)
- Oh, the casinus is much important to... What was it? --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 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. 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. 162.158.91.83 11:23, 12 November 2018 (UTC)
- leading to 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 from or start with and get . Note for all equations except and switching an to a to find , the equations can be correctly derived by treating trig functions as product of single letter variables and algebraically manipulating them. Jimbob (talk) 16:59, 12 November 2018 (UTC)
Is Enchant at target a magic:the gathering reference? 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". --Dryhamm (talk) 21:04, 9 November 2018 (UTC)
- Likely, it refers to the bigbox retailer, Target. 172.68.58.233 (talk) (please sign your comments with ~~~~)
- To me it sounds more like a reference to a nerdy video game, where a certain object worked like this, turning e.g. BEAM OF DARK ENERGY into a BAKED FERRY GNOME 108.162.246.11 21:53, 12 November 2018 (UTC)
- Likely, it refers to the bigbox retailer, Target. 172.68.58.233 (talk) (please sign your comments with ~~~~)
- Voila - s=t. -- Elliott (talk) (please sign your comments with ~~~~)
- That was incredible! (assuming previous poster discovered the extrapolated proof in the description) 172.68.51.154 01:47, 10 November 2018 (UTC)
- Combining and allows you to conclude , not . 162.158.146.10 (talk) (please sign your comments with ~~~~)
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. 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. 162.158.78.166 (talk) (please sign your comments with ~~~~)
Uh... people... THE NAME GAME? Hello? https://en.wikipedia.org/wiki/The_Name_Game 162.158.79.107 (talk) (please sign your comments with ~~~~)
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. 162.158.142.100 04:09, 10 November 2018 (UTC)
141.101.104.71 13:36, 10 November 2018 (UTC) AndreasH
Am I the only one who saw t²n²a⁴ as "tuna"? 172.68.58.233 14:17, 10 November 2018 (UTC)
- Yes. 162.158.75.190 (talk) (please sign your comments with ~~~~)
sex tanks. 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 162.158.123.91 (talk) (please sign your comments with ~~~~)
From when I saw I knew the rest of the comic would be . Observer of the Absurd (talk) 13:28, 15 May 2019 (UTC)