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    1. #1
      Emotionally unsatisfied. Sandform's Avatar
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      Tell me about trigonometric functions

      Tell me anything you know about.

      Radian and degree measure

      Trigonometric functions: (unit Circle)

      Right triangle Trigonometry

      Trigonometric Functions of any angle

      Graphs of sine and Cosine Functions

      Graphs of Other trigonometric Functions

      I am just interested in it, I've already taken trigonometry, but it takes me a bit to get back into the groove heh.

      I actually know alot about all of this, hehe but incase there are things I forgot I wanna know what others think are important from what they remember.

    2. #2
      When the ink runs out... Kushna Mufeed's Avatar
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      A coterminal function is one which is exactly the same as another when graphed.
      e.g. sinA = cos(A - pi/2)
      No wait...coterminal is the wrong word. I've gone blank on the right one.

      Quote Originally Posted by Jeff777 View Post
      I am not sorry or empathetic whatsoever for saying that I believe the world would be much better off without people like you in it. Have a great fucking day.
      [broken link removed]The Dynamics of Segrival[/URL]
      Discuss Segrival here
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    3. #3
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      SOCAHTOA


      All I ever needed for low level British maths.
      Last edited by Carôusoul; 12-18-2007 at 12:59 AM.

    4. #4
      When the ink runs out... Kushna Mufeed's Avatar
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      It's SOH CAH TOA

      Quote Originally Posted by Jeff777 View Post
      I am not sorry or empathetic whatsoever for saying that I believe the world would be much better off without people like you in it. Have a great fucking day.
      [broken link removed]The Dynamics of Segrival[/URL]
      Discuss Segrival here
      See my other [broken link removed]

    5. #5
      Emotionally unsatisfied. Sandform's Avatar
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      Quote Originally Posted by Kushna Mufeed View Post
      A coterminal function is one which is exactly the same as another when graphed.
      e.g. sinA = cos(A - pi/2)
      No wait...coterminal is the wrong word. I've gone blank on the right one.
      Coterminal is when the degree or radian rests on the same line in terms of the circular angle which it is given. I.E.

      75degree's coterminals are -285, +435, +795, - 645 etc...and then if you want them in radians just multiply them by Pi/180.

      Which is what I think you were saying hehe.

    6. #6
      When the ink runs out... Kushna Mufeed's Avatar
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      That's what I was thinking. What's the name for what I was talking about? I think it's cofunction.

      Oh yeah!
      pi/180 radians = 1 degree
      180 degrees/pi = 1 radian

      Quote Originally Posted by Jeff777 View Post
      I am not sorry or empathetic whatsoever for saying that I believe the world would be much better off without people like you in it. Have a great fucking day.
      [broken link removed]The Dynamics of Segrival[/URL]
      Discuss Segrival here
      See my other [broken link removed]

    7. #7
      Emotionally unsatisfied. Sandform's Avatar
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      Not sure...all I know is

      Sine = Cosecant
      secant = Cosine
      Tangent = Cotanget

      each one on the opposite side of the = sine is reverse on the division line. r/t = t/r

      Hehe had to edit after you edited, aye what you said is right.

    8. #8
      On the woad to wuin R.D.735's Avatar
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      Don't forget Euler's formula:


    9. #9
      Emotionally unsatisfied. Sandform's Avatar
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      Quote Originally Posted by R.D.735 View Post
      Don't forget Euler's formula:

      omg!

    10. #10
      When the ink runs out... Kushna Mufeed's Avatar
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      I have never seen that.

      Quote Originally Posted by Jeff777 View Post
      I am not sorry or empathetic whatsoever for saying that I believe the world would be much better off without people like you in it. Have a great fucking day.
      [broken link removed]The Dynamics of Segrival[/URL]
      Discuss Segrival here
      See my other [broken link removed]

    11. #11
      The Wondering Gnome Achievements:
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      Quote Originally Posted by Carôusoul View Post
      SOCAHTOA


      All I ever needed for low level British maths.
      Quote Originally Posted by Kushna Mufeed View Post
      It's SOH CAH TOA

      My teachers tried to teach it to me this way, too. The only problem is, it makes no sense - you end up memorizing a meaningless acronym without understanding the concepts. When it comes time to rederive the formulas and such, you might mix up the letters of the acronym!

      Granted, some things just have to be memorized - conventions and such, and this is quite close to these most basic principles. Still, though, I personally prefer the "COsine means NEXT TO" logic. It's much harder to fuzz up with time.

      Hopefully.

    12. #12
      Emotionally unsatisfied. Sandform's Avatar
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      Quote Originally Posted by thegnome54 View Post

      My teachers tried to teach it to me this way, too. The only problem is, it makes no sense - you end up memorizing a meaningless acronym without understanding the concepts. When it comes time to rederive the formulas and such, you might mix up the letters of the acronym!

      Granted, some things just have to be memorized - conventions and such, and this is quite close to these most basic principles. Still, though, I personally prefer the "COsine means NEXT TO" logic. It's much harder to fuzz up with time.

      Hopefully.
      Damn I was expecting thegnome to reply, but I was also expecting there to be some long post with helpful information. (he usually really good at that lol)

    13. #13
      Cosmic Citizen ExoByte's Avatar
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      Some Old Hippie
      Caught Another Hippie
      Trippin' On Acid

      Now, I don't like those kinda memory things. But my Gr. 10 teacher used that one, and I found it amusing.
      This space is reserved for signature text. A signature goes here. A signature is static combination of words at the end of a post. This is not a signature. Its a signature placeholder. One day my signature will go here.

      Signed,
      Me

    14. #14
      Emotionally unsatisfied. Sandform's Avatar
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      Quote Originally Posted by ExoByte View Post
      Some Old Hippie
      Caught Another Hippie
      Trippin' On Acid

      Now, I don't like those kinda memory things. But my Gr. 10 teacher used that one, and I found it amusing.
      Lol.

    15. #15
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      Quote Originally Posted by Sandform View Post
      Damn I was expecting thegnome to reply, but I was also expecting there to be some long post with helpful information. (he usually really good at that lol)
      Haha, alright, I'll try my hand at explaining radians to you.

      You probably know how degrees work quite well already - take a 90 degree angle, for example.

      A ninety degree angle can be drawn onto a circle so that one quarter of the circle's circumference is penned in, right? This piece of the circumference is called an arc. If you draw a bigger circle, then a ninety degree angle will make a bigger arc - and vice versa. However, no matter how big or small the circle is, a ninety degree angle will always take up the same portion of the circumference - one fourth of it.

      Radians measure the size of this arc (which is the length of the circumference that is 'penned in' by a certain angle placed at the center of the circle, remember) instead of measuring the size of the angle itself. But there's a problem - if you take a big circle versus a smaller one, the arc encompassed by a certain angle will always be larger! How do you make sure that you get the same amount of circumference for a certain angle, no matter how big the circle is?

      The solution is to change your units - instead of measuring in inches or centimeters, you need to use a unit which changes depending on the size of the circle. And, what is the most obvious choice for such a unit? The radius of the circle.

      This makes sense, because the circumference of a circle is 2(pi)radius. This means that there is a linear relationship between radius and circumference. So, you take a big circle (say a radius of 100 units) and a small circle (radius of one unit). You put ninety degree angles in the centers of both. Since the angle takes up a quarter of the circumference of each circle, and the large circle has a circumference of 2(pi)(100), the arc it encompasses on the large circle will be 2(pi)(25). By the same reasoning, the arc on the little circle will be 2(pi)(.25). As you can see, the values are quite different - this is a poor way of telling what angle you're using!

      Here we implement our solution - we count by radii! This gives us 2(pi)(25)/100 for the big circle, which simplifies to 2(pi)(.25), and 2(pi)(.25)/1 for the smaller circle, which simplifies to 2(pi)(.25)! IT WORKS! The values are the same, and you can use this as a measure of angles!

      A radian, then, is the angle which describes a segment of circumference equal to the radius of the circle. Basically, if you took the radius and put it along the outside of the circle, the angle formed when you make lines from the ends of this segment to the center of the circle is called a radian.

      As you know, there are 2(pi)radii in the circumference of any circle. This means that there are 2(pi)radians in a circle, too!

      So, how do you convert from radians into degrees? Well, we know that there are 2(pi)radians in a circle, and we know that there are 360 degrees. It would make sense to divide the former by the latter - (2(pi)radians)/360. This can be simplified, though, by getting rid of the "2" on top. This gives us: pi(radians)/180 = degrees.

      If you want to solve that equation for radians, you get 1 radian = 180/(pi) degrees. This means that a radian is about 57.3 degrees on any circle.

      Hopefully I didn't lose you or oversimplify, I don't really know how far you've been in this area. Enjoy
      Last edited by thegnome54; 12-18-2007 at 02:35 AM.

    16. #16
      Emotionally unsatisfied. Sandform's Avatar
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      Quote Originally Posted by thegnome54 View Post
      This means that a radian is about 57.3 degrees on any circle.

      Hopefully I didn't lose you or oversimplify, I don't really know how far you've been in this area. Enjoy
      Helpful info there. and nope you didn't lose me hehe, oversimplify...lol no, some of the things you could have jumped over in regard to me, but for those just learning it I think that is like the most perfect explanation i've ever heard...probably because my first teach Mr. grey explained it similarly to you, thus I have a predisposition to like it lol.

      Most of the information you guys have given has been review (as it should be for meh heh, i've taken both halves of this already, I just had to do them backwards....I learned the second half first and the first half last)

      Switching around schools all the time takes its toll on you after a while. Damn it all! hehe =P I can't wait till i'm 18 and can legally live on my own.

      Oh well.

    17. #17
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      Trigonometry is not hard, look up the unit circle on wikipedia. Make sure you understand how everything is derived, like how sin theta is equal to y, etc. Also know this identity:



      Quote Originally Posted by R.D.735 View Post
      Don't forget Euler's formula:

      Without which we wouldn't have Euler's identity

    18. #18
      Il Buoиo Siиdяed's Avatar
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      Eurgh, trig. I thought I'd killed this thing back in GCSEs, but it just keeps coming back for more...

      Arm up the Pythagoras, boys.

      a^2 = b^2 + c^2

      Lock and load.

    19. #19
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      I love telling math newbies that e^(j*Pi) = -1... their brains tend to explode just a bit, before they start drooling from the paralysis.

    20. #20
      Emotionally unsatisfied. Sandform's Avatar
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      Quote Originally Posted by Replicon View Post
      I love telling math newbies that e^(j*Pi) = -1... their brains tend to explode just a bit, before they start drooling from the paralysis.
      J is only a variable right? or does it represent something else...like i etc.

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      Quote Originally Posted by Sandform View Post
      J is only a variable right? or does it represent something else...like i etc.
      Yeah he means i

    22. #22
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      Quote Originally Posted by Sandform View Post
      J is only a variable right? or does it represent something else...like i etc.
      j and i are both used. In the engineering world, we use j, mostly to avoid confusion with current (denoted i).

    23. #23
      Dreaming up music skysaw's Avatar
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      How about

      Some Of His Cats Are Hard To Order Alphabetically

      or

      Switch Off His Car And He'll Travel On Air

      or

      Same Old "Hack Club"... Authors Have Tons Of Attitude

      or

      Shake Off Hard Calculus And Hope Trig Offers Answer
      _________________________________________
      We now return you to our regularly scheduled signature, already in progress.
      _________________________________________

      My Music
      The Ear Is Always Correct - thoughts on music composition
      What Sky Saw - a lucid dreaming journal

    24. #24
      Emotionally unsatisfied. Sandform's Avatar
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      What does Cot(90 degree minus (theta)) = ?

      I'm guesing that the answer for what I don't know is Secant...but i'm not sure

      ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

      I know that this =

      Sec (90 degree minus (Theta)) = Cosecant

    25. #25
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      cot (90 - x) = tan ( x )
      sin (90 - x) = cos ( x )
      cos (90 - x) = sin ( x )
      csc (90 - x) = sec ( x )
      sec (90- x) = csc ( x )
      tan (90 - x) = cot ( x )

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