A Conversation for The Trigonometric Laws of Sines and Cosines

Peer Review: A822025 - The Trigonometric Laws of Sines and Cosines

Post 1

#202044

Entry: The Trigonometric Laws of Sines and Cosines - A822025
Author: #202044 - U202044

This is my second submission to the Peer Review forum.

My only regret is not being able to insert diagrams of my own creation to facilitate the understanding of the proofs.

Share and Enjoy.

Regards,
#202044


A822025 - The Trigonometric Laws of Sines and Cosines

Post 2

il viaggiatore

I read as much as I could until I got bored with the math. But that's not to denigrate your entry. It looks quite good and comprehensive. The opening paragrapsh are a very good description.
smiley - ok


A822025 - The Trigonometric Laws of Sines and Cosines

Post 3

Dr Hell

A476606

Unfortunately there is already an Entry on Trigonometry in there, so I think this one is a case for the update HQ.

This entry is very good though. Before you set out to write a new entry try searching h2g2 for already existing entries. I know it's a drag, but that's how it is.

HELL


A822025 - The Trigonometric Laws of Sines and Cosines

Post 4

#202044

There is indeed an edited entry on trigonometry. It hits some of the most basic concepts of trig, such as the unit circle from which the definitions of the trig functions can be derived. It also explains the mnemonic SOH-CAH-TOA, used for memorising the trig functions as ratios of sides in a right triangle.

This particular entry might serve as an addition to that entry...however, I chose not to simply state these Laws but rather rigorously argue their validity, making the entry somewhat more technical in nature for those not merely seeking the light at the end of the tunnel, but also for those who want to examine the cracks in the concrete along the way.

I would be as honored to have this posted as an addition to an existing entry as I would to have it posted as a stand-alone entry. I suppose that a good editor would include a link to the other trig-related entry if this were chosen as a stand-alone selection.

Regards,
#202044


A822025 - The Trigonometric Laws of Sines and Cosines

Post 5

Dr Hell

I see your point 2020...

...and I think you are right. It was just my first impression. When I read this Entry I thought: "Woa, but there was already a good one on trigonometry." I looked it up (and to my shame didn't re-read it) and I was sure that that Entry was quite complete with all rules and all that. That's when I posted the post above. Accept my humble apologies. Your entry is of course closely related to that one, but it goes deeper into the cosine and sine laws. It could perfectly stand alone. You are completely right. Again: Thank you for this excellent and thorough Entry.

HELL


A822025 - The Trigonometric Laws of Sines and Cosines

Post 6

Dr Hell

Well?

Anyone else?

HELL


A822025 - The Trigonometric Laws of Sines and Cosines

Post 7

Tango

Co-incidentaly I am just learning non-right angled trig in school. And that entry seems very good from what i know. One addition I would make though is that the laws are also called rules (Sine Rule and Cosine Rule) you might also want to but the formula for calculateing and angle using cosine rule ( A = Cos^-1((b^2 + c^2 - a^2)/(2bc)) )

(i think, I have just left a maths lesson, but...)

Great entry though,

Tango


A822025 - The Trigonometric Laws of Sines and Cosines

Post 8

Xanadu

I think that this is an excellent piece of writing, going deep into the laws of Sine and Cosine.

The only thing I would like to say is that maybe something could be added about Tangent, the other major Trig. Ratio, or maybe even something about the minor Trig. Ratios: Cosecant (Reciprocal of Sine), Secant (Reciprocal of Cosine), and Cotangent (Reciprocal of Tangent). That would indeed make it a very interesting guide entry indeed...

But still, I love this entry, and I like how it goes in depth about the Sine rule and the Cosine rule, and proving it...very nice.

The ICBM

PS I did not get the minor trig. ratios the wrong way round, it IS like that, though you would think that Cosecant is the reciprocal of Cosine wouldn't you?


A822025 - The Trigonometric Laws of Sines and Cosines

Post 9

#202044

ICBM182:

There are indeed 4 other primary trig functions: tangent, cotangent, secant, and cosecant. But for elementary trigonometry (at least in a first-course trig class setting), there are no equivalent Laws for the other functions. These Laws could be rewritten and finessed so that their reciprocal function counterparts appeared in the Laws instead of sine or cosine, but it would amount to the same basic Laws.

And in reply to the person who suggested that I should mention that these are also referred to as Sine and Cosine Rules: Yes, you are correct. I, however like "Law", simply because I can caress my tender ego into thinking I have more authority when using a "Law" than a "Rule" - HA! The formula that you mentioned, if you take a look at it closely, is a manipulation of the Law of Cosines.

Regards,
#202044


A822025 - The Trigonometric Laws of Sines and Cosines

Post 10

Tango

Yes it is just Cosine Rule with the angle as the subject. I think I said that. I just thought it might to useful to mention it.


A822025 - The Trigonometric Laws of Sines and Cosines

Post 11

#202044

Tango - You were absolutely correct, in that an alternate form of the Law of Cosines can be particularly helpful if one is needing to solve for an angle of the triangle based upon the lengths of the 3 sides. I hope I didn't appear to be shrugging off your suggestion, although I went back and reviewed my initial response and thought I might have made a better go of it.

I incorporated this manipulation of the Law of Cosines into the entry, as well as included the standard warning about how to use the Law in the event that one is given the lengths of the 3 sides (namely - to find the angle opposite the longest side first).

I am also glad to have my computer up and running again so I can see the site.

Regards,
#202044


A822025 - The Trigonometric Laws of Sines and Cosines

Post 12

Sam

Hey there 202044, is this entry ready to go up yet? It's been picked by a scout. Yipee!smiley - smiley


A822025 - The Trigonometric Laws of Sines and Cosines

Post 13

#202044

It's ready as far as I am concerned.

#202044


A822025 - The Trigonometric Laws of Sines and Cosines

Post 14

Sam

It's-a-goin'-in.smiley - smiley


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Post 15

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