Talk:Law of tangents

News · 2 May 2024

new "Alternate Form" section seems off topic

← Previous revision	Revision as of 17:34, 2 May 2024
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::oes either form offer an advantage over the other? I would argue that the smaller tangent law has the advantages of (1) ease of derivation and (2) ease of use to find a missing angle. From a pedagogical perspective the smaller tangent law is immediately understood while the historical law of tangents requires additional interpretation with regards to how one is to supply sums and differences of individuals angles that are not known. I would consider this addition to be similar to showing how to calculate the second root of a quadratic by method other than the quadratic equation -- it is another (and preferable) method. In this case, however, there is not a numerical advantage: there is a conceptual advantage. [[User:Smichr\|Smichr]] ([[User talk:Smichr\|talk]]) 17:19, 2 May 2024 (UTC)	::oes either form offer an advantage over the other? I would argue that the smaller tangent law has the advantages of (1) ease of derivation and (2) ease of use to find a missing angle. From a pedagogical perspective the smaller tangent law is immediately understood while the historical law of tangents requires additional interpretation with regards to how one is to supply sums and differences of individuals angles that are not known. I would consider this addition to be similar to showing how to calculate the second root of a quadratic by method other than the quadratic equation -- it is another (and preferable) method. In this case, however, there is not a numerical advantage: there is a conceptual advantage. [[User:Smichr\|Smichr]] ([[User talk:Smichr\|talk]]) 17:19, 2 May 2024 (UTC)
:::[[User:Smichr\|Smichr]] – my concern is that as far as I can tell "smaller tangent law" is your own made-up name, and I have not seen this identity presented in trigonometry books as related to the law of tangents. Including it here gives the impression that it is a historically important tool that was used in practice by people trying to solve triangles. If that's an accurate impression, then fine it should stay somewhere in Wikipedia (where we could argue about). But if this is something you made up, or someone else made up recently, then it doesn't belong. Cf. [[Wikipedia:Original research]].	:::[[User:Smichr\|Smichr]] – my concern is that as far as I can tell "smaller tangent law" is your own made-up name, and I have not seen this identity presented in trigonometry books as related to the law of tangents. Including it here gives the impression that it is a historically important tool that was used in practice by people trying to solve triangles. If that's an accurate impression, then fine it should stay somewhere in Wikipedia (where we could argue about). But if this is something you made up, or someone else made up recently, then it doesn't belong. Cf. [[Wikipedia:Original research]].
:::: {{tq\|i=yes\|"Both forms aim to solve the problem of determining angles from the given angle and sides [...] the problem is not how to write an expression using sums and differences of angles"}} – the law of tangents was used in a variety of ways by a variety of authors. It's overly reductive to claim that it had only one narrow purpose. (But our article here should do a better job of describing its history.)
:::: {{tq\|i=yes\|"showing how to calculate the second root of a quadratic by method other than the {{bracket\|[[quadratic formula]]}}"}} – I can find many sources directly discussing how to calculate roots of quadratic equations by various methods, which is why it's fine for Wikipedia to include a discussion of that topic in {{slink\|Quadratic formula#Numerical calculation}}. –[[user:jacobolus\|jacobolus]] [[User_talk:jacobolus\|(t)]] 17:25, 2 May 2024 (UTC)	:::: {{tq\|i=yes\|"showing how to calculate the second root of a quadratic by method other than the {{bracket\|[[quadratic formula]]}}"}} – I can find many sources directly discussing how to calculate roots of quadratic equations by various methods, which is why it's fine for Wikipedia to include a discussion of that topic in {{slink\|Quadratic formula#Numerical calculation}}. –[[user:jacobolus\|jacobolus]] [[User_talk:jacobolus\|(t)]] 17:25, 2 May 2024 (UTC)

Okumaya devam et...

← Previous revision	Revision as of 17:34, 2 May 2024
Line 132:	Line 132:
::oes either form offer an advantage over the other? I would argue that the smaller tangent law has the advantages of (1) ease of derivation and (2) ease of use to find a missing angle. From a pedagogical perspective the smaller tangent law is immediately understood while the historical law of tangents requires additional interpretation with regards to how one is to supply sums and differences of individuals angles that are not known. I would consider this addition to be similar to showing how to calculate the second root of a quadratic by method other than the quadratic equation -- it is another (and preferable) method. In this case, however, there is not a numerical advantage: there is a conceptual advantage. [[User:Smichr\|Smichr]] ([[User talk:Smichr\|talk]]) 17:19, 2 May 2024 (UTC)	::oes either form offer an advantage over the other? I would argue that the smaller tangent law has the advantages of (1) ease of derivation and (2) ease of use to find a missing angle. From a pedagogical perspective the smaller tangent law is immediately understood while the historical law of tangents requires additional interpretation with regards to how one is to supply sums and differences of individuals angles that are not known. I would consider this addition to be similar to showing how to calculate the second root of a quadratic by method other than the quadratic equation -- it is another (and preferable) method. In this case, however, there is not a numerical advantage: there is a conceptual advantage. [[User:Smichr\|Smichr]] ([[User talk:Smichr\|talk]]) 17:19, 2 May 2024 (UTC)
:::[[User:Smichr\|Smichr]] – my concern is that as far as I can tell "smaller tangent law" is your own made-up name, and I have not seen this identity presented in trigonometry books as related to the law of tangents. Including it here gives the impression that it is a historically important tool that was used in practice by people trying to solve triangles. If that's an accurate impression, then fine it should stay somewhere in Wikipedia (where we could argue about). But if this is something you made up, or someone else made up recently, then it doesn't belong. Cf. [[Wikipedia:Original research]].	:::[[User:Smichr\|Smichr]] – my concern is that as far as I can tell "smaller tangent law" is your own made-up name, and I have not seen this identity presented in trigonometry books as related to the law of tangents. Including it here gives the impression that it is a historically important tool that was used in practice by people trying to solve triangles. If that's an accurate impression, then fine it should stay somewhere in Wikipedia (where we could argue about). But if this is something you made up, or someone else made up recently, then it doesn't belong. Cf. [[Wikipedia:Original research]].
:::: {{tq\|i=yes\|"Both forms aim to solve the problem of determining angles from the given angle and sides [...] the problem is not how to write an expression using sums and differences of angles"}} – the law of tangents was used in a variety of ways by a variety of authors. It's overly reductive to claim that it had only one narrow purpose. (But our article here should do a better job of describing its history.)
:::: {{tq\|i=yes\|"showing how to calculate the second root of a quadratic by method other than the {{bracket\|[[quadratic formula]]}}"}} – I can find many sources directly discussing how to calculate roots of quadratic equations by various methods, which is why it's fine for Wikipedia to include a discussion of that topic in {{slink\|Quadratic formula#Numerical calculation}}. –[[user:jacobolus\|jacobolus]] [[User_talk:jacobolus\|(t)]] 17:25, 2 May 2024 (UTC)	:::: {{tq\|i=yes\|"showing how to calculate the second root of a quadratic by method other than the {{bracket\|[[quadratic formula]]}}"}} – I can find many sources directly discussing how to calculate roots of quadratic equations by various methods, which is why it's fine for Wikipedia to include a discussion of that topic in {{slink\|Quadratic formula#Numerical calculation}}. –[[user:jacobolus\|jacobolus]] [[User_talk:jacobolus\|(t)]] 17:25, 2 May 2024 (UTC)

Talk:Law of tangents

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