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#1 Re: Help Me ! » Why are trig functions taught as being blackboxes? » 2018-05-08 05:26:02

Apologies for not replying after you gave that explanation.  It is a good explanation.  Thanks.

#2 Re: Help Me ! » Why are trig functions taught as being blackboxes? » 2018-03-01 05:59:55

Possibly causing even more confusion, we might see this:

f(x) = sin(x)

What we have in that notation is nothing but one label being equivalent to another label.  No operations are present.

#3 Re: Help Me ! » Why are trig functions taught as being blackboxes? » 2018-03-01 05:54:49

Expanding on the above post.

For some function, f(x) = x^2, for example:

f(x), is a label for a function.  It is not the operations of a function.
x^2, is the operation of the function.  It is what the function does.

For the sin function, sin(angle) = opposite/hypotenuse:

sin(angle), is also only a label for a function.  Is is not the operations of the function.
opposite/hypotenuse, is a ratio (a number) that is equivalent to the result of the operations of the sin function.
The actual operations of the sin function are not represented in the notation.

But both of the above are notated as if having the same general form:  A label and operation(s).

f(x) = x^2
sin(angle) = opposite/hypotenuse

And at least for all the trig resources which I have seen, a distinction is never made that different things are being represented by the same notation form.  That seems like a disaster in waiting for students of trig.

#4 Help Me ! » Why are trig functions taught as being blackboxes? » 2018-03-01 04:54:44

Replies: 4

Why is trigonometry taught from the perspective of trig functions being blackboxes?  It seems to be counter to what math is about.

Given some function, f(x) = some calculation involving x, we see what the function is and does.  For example, given the function, f(x) = x^2, we see that the function squares x.

But given a trig function, for example, sin(angle) = opposite/hypotenuse, we don't actually see what the function is and does.  sin() is a blackbox, and we don't see what it does to the angle.  And possibly creating much confusion here is that the notation used for trig functions can make it appear that, opposite/hypotenuse, is the operation of the function.

#5 Re: Maths Teaching Resources » Maths Books » 2017-11-18 07:43:30

greg1313 wrote:

iamaditya, it has been four and a half months since your last reply to bobbym, who has since died.

The answer to # 15 is log(12).

That is news to me.  I didn't know bobbym, but he helpfully replied to some of my posts here.  RIP.

#7 Re: Maths Teaching Resources » Free Computer Algebra Systems? » 2017-11-06 07:12:13

Geogebra has been a very helpful learning environment, although it does have some annoying quirks, as I'm sure other tools do.  Also, I have only tinkered a tad bit with Gnu Octave, but going on what little I have used of it, it seems very promising.  After I get a little further along in my self-education of math and programming, I intend to give Octave a proper exploration.

#8 Maths Teaching Resources » Book on math fundamentals » 2017-11-06 06:53:47

Replies: 1

Over the last year I have picked up a handful of math books, looking to better my understanding of math fundamentals before going further.  One of those books which I have found to be excellent in clarifying concepts of fundamental topics is,  Yes, But Why?  Teaching for understanding in mathematics, Ed Southall.

This book is obviously aimed at teachers, but as an independent learner I have found it to be an excellent resource for getting a solid birdseye view of various topics and how things work.  I only wish that it existed long ago (it was released earlier this year), as I have wasted alot of time over the years digging through various resources, often running in circles and hitting walls or becoming bored to death.  The book begins at arithmetic and graduates through topics in algebra, geometry, and ends with fundamentals in trigonometry.

What I like about it:

- It gets right to the point of concepts without burrying the reader in a bunch of fluff or too much detail from the getgo.
- It doesn't focus on procedures over concepts.
- It makes good connections from one topic to the next, not leaving gaping holes in understanding.
- Reading it has been a series of 'Ah, ha' moments without the brickwalls of so many other resources.
- It makes good use of graphics for explaining concepts; doesn't include graphics for the sake of dressing things up.
- It isn't stodgy in style; it is very conversational in style.  It is an educational and fun read at the same time.
- It makes many mentions of where math terms come from and how they relate to the topic at hand, along with other historical bits.
- It is (along with many articles at MathisFun) what I feel in many ways, how math should be taught.

I am not associated with this book in any way.  Just sharing a resource that I have found to be exceptional among math books as an adult self-learner relearning math fundamentals.  This book, along with MathisFun, Geogebra, and exploring using a compass and rule (because working with my hands is often more satisfying) have been time well spent.  I am finding myself to be a visual learner, where numbers often are only added precision in application of concepts.

#9 Re: Computer Math » Geogebra: Why does sin() give the wrong value? » 2017-11-06 04:56:10

Answered by a member at  the Geogebra forum.  Degrees must be indicated within the function.  The angle unit setting in Geogebra's preferences is for the display of graphics only; not for setting input value units of those functions which expect angle values as the input, such as sin(), cos(), tan().

The degree symbol must be entered following the degree number.  A popup window with symbols can be brought up by clicking the button in the far left of the input box, where the degree symbol can be found at the bottom of the window (in Geogebra 5).

I think my point of confusion stemmed from the angle unit setting.  When setting the angle unit in a calculator, any functions which expect angle values will use that angle unit setting, where in Geogebra, only graphing is affected by the angle unit setting.  Also in Geogebra, there is nothing in the preferences window stating that the angle unit setting only affects graphing.

#10 Computer Math » Geogebra: Why does sin() give the wrong value? » 2017-11-06 04:06:08

Replies: 3

To present this as simply as possible, say I have a right triangle with sides: adjacent = 0.71; opposite = 0.71; hypotenuse = 1. The angle theta is 45 degrees. When I enter in the input box, sin(45) , I get 0.85, which is obviously not the sine of 45 degrees.

Am I doing something wrong here?  In case it is relevant, I am using Geogebra 5 with the angle unit set to degrees.

#11 Re: Help Me ! » Word Problems: Multiplying Fractions » 2017-01-17 03:46:01

Obviously, you want 1/2 of 3/4 of old fashioned oats for making 1/2 of the recipe.  Maybe what it isn't so obvious is that division by 2 gives the same result as multiplication by 1/2: 

To make sense of the above, remember that any number can be rewritten as the number over 1...

...and to get half of something, we have to divide it by 2...

...which can be rewritten as a multiplication...

And so...

#12 Re: Help Me ! » The quadratic formula » 2017-01-11 08:16:03

Bob, that is a very clear explanation.  Thanks for taking the time.

#13 Help Me ! » The quadratic formula » 2017-01-10 16:41:08

Replies: 2

I came across a video in which the author explains visually how to arrive at the quadratic formula, except he skips some steps.

Here is the video:

I follow it up to this point, where some steps are skipped:

In the video, the right side of the equation goes from: 


So I think that I can rewrite the first example like this: 

But I don't see how the a can be moved to the numerator.  Or maybe I'm approaching it all wrong.

By the way, I really like this approach to explaining math.  I never understood what 'completeing the square' actually means until I saw this video.  It seems right at home with so many of the nice explanations here at Math is Fun.

Side note:  I really appreciate the LaTeX integration in the forum.  This is nice!

#14 Re: Dark Discussions at Cafe Infinity » What is EM? » 2016-12-19 06:01:27

Agnishom wrote:

I like writing too. Have you seen my notes?

They could be hidng in a piano, or other such place.

#15 Re: Dark Discussions at Cafe Infinity » What is EM? » 2016-12-18 20:20:18

Agnishom wrote:


A main ingredient in ghoul gravy, which gained popularity shortly after the development of the modern crematory.


#16 Dark Discussions at Cafe Infinity » What is EM? » 2016-12-18 12:54:03

Replies: 66

I assume that it is an abbreviation for, <something> math.

#18 Computer Math » Plotting vertical line in Geogebra? » 2016-12-12 06:41:28

Replies: 3

I'm relearning algebra after some years of being away from school, and I'm learning to use Geogrebra.  At the moment I'm plotting some lines to get a sense of what elementary functions look like on a grid.  I never really got a good sense of this when I was in school.

So I have:

f(x) = x , which gives a diaganol line.
f(x) = -x , which gives a mirror of the above diagonal line (Is there a math term for this?).
f(x) = 0x , which gives a horizontal line.

How would I plot a vertical line?  The closest that I have found is:

f(x) = 10^(100)x

#19 Introductions » Hello people of mathisfun » 2016-12-12 06:27:39

Replies: 3

Great site.  I have been visiting here sporadically over a couple of years, and it is always a good experience.  I guess it is about time that I joined the forum.  Thanks to everyone who contributes to the site and discussion on the forum.

About myself:  I am an adult who never learned much math outside of basic algebra.  I am going back and relearning algebra, looking at going much further.  My interests in math stem from interests in music, electronics, programming, carpentry, and other areas.  And I am coming around to finding out that math is interesting in it's own right.

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