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.

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.

SOCAHTOA


All I ever needed for low level British maths.

It's SOH CAH TOA

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Originally Posted by Kushna Mufeed

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.

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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.

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

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.

Don't forget Euler's formula:

http://upload.wikimedia.org/math/1/8...0d1d44a58c.png

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Originally Posted by R.D.735

Don't forget Euler's formula:

http://upload.wikimedia.org/math/1/8...0d1d44a58c.png

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omg!

I have never seen that.

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Originally Posted by Carôusoul

SOCAHTOA


All I ever needed for low level British maths.

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Quote:

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Originally Posted by Kushna Mufeed

It's SOH CAH TOA

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:lol::lol:
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. ;)

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Originally Posted by thegnome54

:lol::lol:
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. ;)

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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)

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.

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Originally Posted by ExoByte

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.

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Lol.

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Originally Posted by Sandform

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)

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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 :)

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Originally Posted by thegnome54

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 :)

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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.

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:

http://upload.wikimedia.org/math/6/8...fe59e2bf0d.png

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Originally Posted by R.D.735

Don't forget Euler's formula:

http://upload.wikimedia.org/math/1/8...0d1d44a58c.png

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Without which we wouldn't have Euler's identity :)

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.

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.

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Originally Posted by Replicon

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.

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J is only a variable right? or does it represent something else...like i etc.

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Originally Posted by Sandform

J is only a variable right? or does it represent something else...like i etc.

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Yeah he means i

Quote:

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Originally Posted by Sandform

J is only a variable right? or does it represent something else...like i etc.

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j and i are both used. In the engineering world, we use j, mostly to avoid confusion with current (denoted i).

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

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

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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Originally Posted by wasup

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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:hug:

You don't need to memorize all that. All you need to know is the definitions of the other trig functions, which are all in terms of sin and cos:

sec(90-x) = 1/cos(90-x) = 1/sin(x) = csc(x)

........or, just realize that coX goes with X :P

I pretty much just spent about 2 months in my pre-calc class extensively covering trigonometric functions, all their uses, and many side things (still doing more stuff on them).

So if you have any specific questions, just post here, PM me, or IM me. I'd be glad to help :)

I want to add why the trigonometric functions are what they are. Teachers pretty much teach how to use them and almost never explain what in the world they are. When teachers don't do that, it makes math look like a whole lot of random weirdness being forced onto students for no apparent reason. I believe in explaining the reasons for the rules so math will seem like the rational subject it is.

The trigonometric functions are all about how all triangles with any two given angle measures are similar (Because the third set of angles will automotically be congruent if the other two are.). When triangles are similar, their corresponding sides are proportional. Therefore, all triangles with a 90 degree angle and a (for example) 40 degree angle are going to have exactly the same shape and be similar (Since the third angle will always be 50 degrees.), which means that the ratio of the measures of the side opposite the 40 degree angle and the hypotenuse will be the same for every single triangle with a 90 degree angle and a 40 degree angle. That ratio is the sine of 40 degrees, which is also the cosine of 50 degrees. Because those ratios are always the same, they can be used to find side and angle measures if enough other information is given.

Another way to remember sine, cosine, and tangent is to learn those three words in order and then remember, "Oscar had a hit of acid." I was taught, "... hunk of apples," but the acid one sticks better.

sine: opposite/hypotenuse
cosine: adjacent/hypotenuse
tangent: opposite/adjacent

anyone have an answer for this question? More of a physics problem though heh.

A 15 N force directed to the west acts on an object for 3.0 seconds, what is the change in momentum of the object?


(while your at it...)

A car is moving in uniform circular motion. If the car's speed were to double to keep the car moving with the same radius the acceleration would what?

increase by a factor of 2

Or by a factor of 4?

Let m be the mass.

F = m*a --> a = F/m

So the change in velocity will be 3*(F/m), so the change in momentum will be 3*(F/m)*m = 3*F.

For the second question... for chrissake, there's no thinking involved. Just plug the damn thing into the equation :P

I won't look it up, but IIRC, the centripetal acceleration is something like v^2 / r

If the speed were to double, you'd have (2*v)^2 / r = 4 * v^2/4, i.e. factor of 4.


Now that I've shown that this is so easy someone who hasn't touched it in years can do it in his head while typing on a dreaming forum, I won't solve any more homework questions that are clearly "plug it into one equation", for that would be wrong. This stuff is for YOUR own good. Think about it before giving up. I'll happily help you along and stuff, but at the very least, apply a systematic "what do I know about this system? ok, now given the information I have, what can I figure out about it that would help me find the answer to this question?" type approach before posting it.

New problem...

sinx(1 - 2(cos^2)x + (Cos^4)x) = (sin^5)x meanwhile i'll be trying to figure it out myself heh.

Oh I figured it out, turns out all you have to do is realize that sin^4x = (sin^2x)(sin^2x) = (-cot^2x +1)(-cot^2x +1) = cos^4x - 2cos^2x + 1 which is means that since cos^4x - 2cos^2x + 1 = sin^4x, when multiplied by sin, sin(cos^4x - 2cos^2x + 1) becomese sin^5x

Please help me with these (any of these) it has been a long time since I went back and did any of these and I seriously need the help. I need it quick too =P.


find the inverse of x/(x+3)

Find all real and imaginary zeros of f(x) = x^3 + x^2 + 13x - 15 given that 1 is a zero of the function.

find the inverse of 3x+2

Find the range of the function f(x) = 3^(x+9) + 4

State the domain of the function f(x) = log(3)(x-4)

List the exact amplitude period and horizontal shift of y = 2tan(pix+3)

amplitdue period horizontal shift and vertical shift of y = 2cos[3x-pi/2] + 4

find exact value of vertical asymptotes for 0 < theta < for the function y = cot(3theta)