# Law of cosines is defeating me :(

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**1**la vache fantôme

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**Law of cosines is defeating me :(**

aaah this is hard. These law of cosine things, sheesh they make an equation too large for my to handle i dont know where to start . Anybody have any hints?

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could you elaborate alittle more on what equations your talking about?

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certainly. Infact i will draw out the problem in autocad or something

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I just did this in school myself. I'll be the first to tell you I'm not a math guy, but if you can explain the problem a little more maybe I can help.

Are you having a problem with the formula or its application?

Are you having a problem with the formula or its application?

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alright im doing a quick drawing in paint

hold on (5 minutes)

hold on (5 minutes)

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AAAAH.

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aaargh ive always hated math beyond multiplication, proofs, addition, subtraction and division but this....oooooooo this is beyond hate! Im so close to wanting to destroy something.

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If you look in your book, you should find a formula where you can use the sides to find the angles. Trig is the easier of the Algebra/Trigonometry/Calculus trifecta of higher math.

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algebra sucked, but not nearly as bad as this. See heres the scoop, my math teacher is the biggest math geek i know. He teaches most of the higher math classes. Part of the geometry curiculum is a 4 day intro to the very basics of trig. This guy loves trig and not geometry. He always goes way beyond what is required and faster than any other class. SO we are 3 weeks ahead of the curiculum. So hes spending 4 weeks instead of 4 days . And i hate it already and its just been a week. Past precalc im not wanting to take any more classes of math.

So far in engineering i have used only basic math and a fine calculator from texas instruments

So far in engineering i have used only basic math and a fine calculator from texas instruments

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and my book is a geometry book, it only has the very bare stuff like cos sin tan stuff

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I'd look for a different vocation. Lot's of math in engineering - especially calculus.

2nd semester calc, you gotta know trig cold.

sun

2nd semester calc, you gotta know trig cold.

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is this supposed to be a right triangle?

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I see myself with a mighty TI89, the calculator thats banned from DHS math dept. but who gives a rats petoot in the eng lab . *sigh* but i guess im gonna end up taking all this crap anyways despite how much i hate it. Its the one class this year I have to work at with effort and im a lazy person, not a good blend

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its not supposed to be a rt triangle

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Originally Posted by

**phantomcow2**its not supposed to be a rt triangle

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i wish it was a rt triangle, i can solve those like a machine . He said something about making an imaginary line from the apex of the triangle down, so that it meets the base at a 90 degree angle and calling that segment h. Then applying law of cosines to find the sides or something. aaah the more i think about it, the more i get confused

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Aw come on. This stuff you should know like the back of your hand. Just practice a bit more.

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I just started it so i dont know. He taught us law of cosine and sine friday and said "here, do this for homework" I wish i knew it, im at a stall though i have no idea what to do

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and to add to the fun, he said if we dont have it done we have an hours detention.

pffft...screw that, i did work and thats good enough

pffft...screw that, i did work and thats good enough

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Law of cosines -- no worries. It's GREAT, it's EASY and you don't have to worry about making sure you're dealing with a fracking right triangle.

You know Pythagorean theorem: c^2 = a^2 + b^2? That's easy. That's for right triangles. Law of cosines is the SAME THING without having to worry about it being a right triangle!

c^2 = a^2 + b^2 - 2ab cos angleC

If this were a right triangle, then the angleC would be 90 degrees, and you'd get the Pythagorean theorem. The 2ab cos angleC is the "fudge factor" that lets you adjust for the non-rightedness of the triangle.

Seriously, it's that easy. You know the Pythagorean Theorem. So use it. Then all you have to remember is that if your angle C isn't 90 degrees, if you're not playing with a right triangle, you have to subtract 2 * a * b * cos Cangle.

If you read nothing else, read this:

MOST MATH TEACHERS DON'T TELL YOU HOW TO KNOW WHEN TO USE ALL THEIR STUPID FORMULAS. This is an engineer who learned the hard way.

You need a cheat sheet. Not for tests, but for doing your homework. Write down all the formulas in the unit, then right by them write what they're good for. Here's a quick one.

Pythagorean theorem. c^2 = a^2 + b^2. Rt. triangle, use lengths of 2 sides to find length of 3rd

Law of sines a/sin A = b/sin B = c/sin C = 2R Any triangle, relationship between size of angle and length of it's opposing side

Law of cosines: (above) : length of all 3 sides and size of one angle: find whichever one's missing.

So you use the law of Sines and law of Cosines together a lot. Like in your homework -- you have the length of all 3 sides and you need to know the angles. Check your cheat sheet -- you can find ONE angle with the law of cosines. So then you've got that angle. Now you need other angles. You can use the law of cosines again -- chug through -- or you can check the law of sines. Your cheat sheet says "relationships between side lengths and angles" and you KNOW the side lengths, and you know ONE angle. So one of the entries in the equal sign series is a number you can find. So you can use it to find the rest.

So math isn't hard, it's just frequently taught crappily. Formulas are just tools. Equal signs are just equal signs. I could multiply both sides by a million if I wanted to, but it wouldn't be useful. Formulas and theorems like this are just tools to use when you want to do something useful. If you've got a bike with a pedal attached and you want to take it off, use a pedal wrench. If you've got a triangle with all the side lengths and you want to know an angle, use the law of cosines. It's not as mechanical and easy to see, but after you get the trick it's not a problem. It's like seeing one of those "magic eye" pictures -- after it clicks it's much easier to get the next one.

Good luck.

PS: Engineering sucks though.

/Engineering grad student

You know Pythagorean theorem: c^2 = a^2 + b^2? That's easy. That's for right triangles. Law of cosines is the SAME THING without having to worry about it being a right triangle!

c^2 = a^2 + b^2 - 2ab cos angleC

If this were a right triangle, then the angleC would be 90 degrees, and you'd get the Pythagorean theorem. The 2ab cos angleC is the "fudge factor" that lets you adjust for the non-rightedness of the triangle.

Seriously, it's that easy. You know the Pythagorean Theorem. So use it. Then all you have to remember is that if your angle C isn't 90 degrees, if you're not playing with a right triangle, you have to subtract 2 * a * b * cos Cangle.

If you read nothing else, read this:

MOST MATH TEACHERS DON'T TELL YOU HOW TO KNOW WHEN TO USE ALL THEIR STUPID FORMULAS. This is an engineer who learned the hard way.

You need a cheat sheet. Not for tests, but for doing your homework. Write down all the formulas in the unit, then right by them write what they're good for. Here's a quick one.

Pythagorean theorem. c^2 = a^2 + b^2. Rt. triangle, use lengths of 2 sides to find length of 3rd

Law of sines a/sin A = b/sin B = c/sin C = 2R Any triangle, relationship between size of angle and length of it's opposing side

Law of cosines: (above) : length of all 3 sides and size of one angle: find whichever one's missing.

So you use the law of Sines and law of Cosines together a lot. Like in your homework -- you have the length of all 3 sides and you need to know the angles. Check your cheat sheet -- you can find ONE angle with the law of cosines. So then you've got that angle. Now you need other angles. You can use the law of cosines again -- chug through -- or you can check the law of sines. Your cheat sheet says "relationships between side lengths and angles" and you KNOW the side lengths, and you know ONE angle. So one of the entries in the equal sign series is a number you can find. So you can use it to find the rest.

So math isn't hard, it's just frequently taught crappily. Formulas are just tools. Equal signs are just equal signs. I could multiply both sides by a million if I wanted to, but it wouldn't be useful. Formulas and theorems like this are just tools to use when you want to do something useful. If you've got a bike with a pedal attached and you want to take it off, use a pedal wrench. If you've got a triangle with all the side lengths and you want to know an angle, use the law of cosines. It's not as mechanical and easy to see, but after you get the trick it's not a problem. It's like seeing one of those "magic eye" pictures -- after it clicks it's much easier to get the next one.

Good luck.

PS: Engineering sucks though.

/Engineering grad student

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Originally Posted by

**RedHairedScot**Law of cosines -- no worries. It's GREAT, it's EASY and you don't have to worry about making sure you're dealing with a fracking right triangle.

You know Pythagorean theorem: c^2 = a^2 + b^2? That's easy. That's for right triangles. Law of cosines is the SAME THING without having to worry about it being a right triangle!

c^2 = a^2 + b^2 - 2ab cos angleC

If this were a right triangle, then the angleC would be 90 degrees, and you'd get the Pythagorean theorem. The 2ab cos angleC is the "fudge factor" that lets you adjust for the non-rightedness of the triangle.

Seriously, it's that easy. You know the Pythagorean Theorem. So use it. Then all you have to remember is that if your angle C isn't 90 degrees, if you're not playing with a right triangle, you have to subtract 2 * a * b * cos Cangle.

If you read nothing else, read this:

MOST MATH TEACHERS DON'T TELL YOU HOW TO KNOW WHEN TO USE ALL THEIR STUPID FORMULAS. This is an engineer who learned the hard way.

You need a cheat sheet. Not for tests, but for doing your homework. Write down all the formulas in the unit, then right by them write what they're good for. Here's a quick one.

Pythagorean theorem. c^2 = a^2 + b^2. Rt. triangle, use lengths of 2 sides to find length of 3rd

Law of sines a/sin A = b/sin B = c/sin C = 2R Any triangle, relationship between size of angle and length of it's opposing side

Law of cosines: (above) : length of all 3 sides and size of one angle: find whichever one's missing.

So you use the law of Sines and law of Cosines together a lot. Like in your homework -- you have the length of all 3 sides and you need to know the angles. Check your cheat sheet -- you can find ONE angle with the law of cosines. So then you've got that angle. Now you need other angles. You can use the law of cosines again -- chug through -- or you can check the law of sines. Your cheat sheet says "relationships between side lengths and angles" and you KNOW the side lengths, and you know ONE angle. So one of the entries in the equal sign series is a number you can find. So you can use it to find the rest.

So math isn't hard, it's just frequently taught crappily. Formulas are just tools. Equal signs are just equal signs. I could multiply both sides by a million if I wanted to, but it wouldn't be useful. Formulas and theorems like this are just tools to use when you want to do something useful. If you've got a bike with a pedal attached and you want to take it off, use a pedal wrench. If you've got a triangle with all the side lengths and you want to know an angle, use the law of cosines. It's not as mechanical and easy to see, but after you get the trick it's not a problem. It's like seeing one of those "magic eye" pictures -- after it clicks it's much easier to get the next one.

Good luck.

PS: Engineering sucks though.

/Engineering grad student

You know Pythagorean theorem: c^2 = a^2 + b^2? That's easy. That's for right triangles. Law of cosines is the SAME THING without having to worry about it being a right triangle!

c^2 = a^2 + b^2 - 2ab cos angleC

If this were a right triangle, then the angleC would be 90 degrees, and you'd get the Pythagorean theorem. The 2ab cos angleC is the "fudge factor" that lets you adjust for the non-rightedness of the triangle.

Seriously, it's that easy. You know the Pythagorean Theorem. So use it. Then all you have to remember is that if your angle C isn't 90 degrees, if you're not playing with a right triangle, you have to subtract 2 * a * b * cos Cangle.

If you read nothing else, read this:

MOST MATH TEACHERS DON'T TELL YOU HOW TO KNOW WHEN TO USE ALL THEIR STUPID FORMULAS. This is an engineer who learned the hard way.

You need a cheat sheet. Not for tests, but for doing your homework. Write down all the formulas in the unit, then right by them write what they're good for. Here's a quick one.

Pythagorean theorem. c^2 = a^2 + b^2. Rt. triangle, use lengths of 2 sides to find length of 3rd

Law of sines a/sin A = b/sin B = c/sin C = 2R Any triangle, relationship between size of angle and length of it's opposing side

Law of cosines: (above) : length of all 3 sides and size of one angle: find whichever one's missing.

So you use the law of Sines and law of Cosines together a lot. Like in your homework -- you have the length of all 3 sides and you need to know the angles. Check your cheat sheet -- you can find ONE angle with the law of cosines. So then you've got that angle. Now you need other angles. You can use the law of cosines again -- chug through -- or you can check the law of sines. Your cheat sheet says "relationships between side lengths and angles" and you KNOW the side lengths, and you know ONE angle. So one of the entries in the equal sign series is a number you can find. So you can use it to find the rest.

So math isn't hard, it's just frequently taught crappily. Formulas are just tools. Equal signs are just equal signs. I could multiply both sides by a million if I wanted to, but it wouldn't be useful. Formulas and theorems like this are just tools to use when you want to do something useful. If you've got a bike with a pedal attached and you want to take it off, use a pedal wrench. If you've got a triangle with all the side lengths and you want to know an angle, use the law of cosines. It's not as mechanical and easy to see, but after you get the trick it's not a problem. It's like seeing one of those "magic eye" pictures -- after it clicks it's much easier to get the next one.

Good luck.

PS: Engineering sucks though.

/Engineering grad student

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Like Scot said, C^2=A^2+B^2-2AB Cos<c

So for you if you wanted to find say, <Gamma

4^2=8^2+5^2-2*8*5*Cos<Gamma

You'd carry out all that crap and work it down to isolate <Gamma

Don't worry, I'm not a math guy myself in any way and I've managed to figure most of this out.

So for you if you wanted to find say, <Gamma

4^2=8^2+5^2-2*8*5*Cos<Gamma

You'd carry out all that crap and work it down to isolate <Gamma

Don't worry, I'm not a math guy myself in any way and I've managed to figure most of this out.

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cosine is just the inverse of sine like if sine was 33/65 then cosine is 65/33(read 65 over 33). and sine is opposite side over hypotinuse I think wait forget that I'm too tired but I have a kick butt trig book that I got from a second hand store, after I was out of school, that made me go "Wow this is easy, the public school system really does suck as$."

Then I was watching this education expert professer dude on the tele and he was like mathbooks in this country suck then as a good example he described european and japanese math books.

Well that kickass book I got, it matches the description of the japanese and euro texts which is "readable, no masses of sidebars, bubbles, worthless trivia, random reveiw sections, or endless lists of problems" (like cramming it in harder with more problems is going to do any good when you don't understand it in the first place. Bigger hammer, the american way.) So the book is written so it can be read, now get this, like a book, real paragraphs and everything with an occational picture and problem as an example, and two or three practice problems at the end of the chapter. it covers a whole trig course, clearly, in about 120 6"x10" black and white pages.

I'll get it out tomarrow and look up laws of sine/cosine tangent/cotangent secant/cosecant

Then I was watching this education expert professer dude on the tele and he was like mathbooks in this country suck then as a good example he described european and japanese math books.

Well that kickass book I got, it matches the description of the japanese and euro texts which is "readable, no masses of sidebars, bubbles, worthless trivia, random reveiw sections, or endless lists of problems" (like cramming it in harder with more problems is going to do any good when you don't understand it in the first place. Bigger hammer, the american way.) So the book is written so it can be read, now get this, like a book, real paragraphs and everything with an occational picture and problem as an example, and two or three practice problems at the end of the chapter. it covers a whole trig course, clearly, in about 120 6"x10" black and white pages.

I'll get it out tomarrow and look up laws of sine/cosine tangent/cotangent secant/cosecant

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Originally Posted by

**capsicum**cosine is just the inverse of sine

1/sin = cosecant = csc

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Redhaiedscott got it right, just thought I'd add a comment that might make the law of cos seem more familiar. You could use it for a rt. triangle because the cos(90) is 0 so the payth. therom is mearly a special case of the law of cos.

To learn math you must calm down and just do lots of poblems. Any time you take a math class go buy the Schaum's Outline. After 40 years of engineering I still buy one once in a while if I need to learn something new (long ago tired of classes).

Joe

To learn math you must calm down and just do lots of poblems. Any time you take a math class go buy the Schaum's Outline. After 40 years of engineering I still buy one once in a while if I need to learn something new (long ago tired of classes).

Joe