Math Is Fun Forum

Hi Dave

Your log fire reminded me of the following:

bob

hi nha,

Not my best subject but, as no one else is posting I'll throw in my ideas.

(ii) first.  I think you've got to show symmetric, reflexive and transitive. 

So, for example, define R so that a R b. when a and b are both in Si. 

As  a in Si and b in Si => b in Si and a in Si => b R a so it is reflexive.

(i)  ??? What ordered pairs is this question after?  I really cannot get this.  Sorry.  Do you have a given example already to show what this means?

Bob

Hi bobbym,

Thank you for posting on this.  At least I can feel as though someone is 'out there'.  This is an excellent example of what we were saying earlier.

He posted new questions faster than I could respond.

What puzzles me is the spread of levels of difficulty.  From basic sine work through to a fairly complex circumcircle question which took me a page of working, using two advanced trig formulas followed by a binomial expansion.  I'm not claiming that's the only way to do the problem but, however you do it, it's several orders of magnitude harder than "why is sin 0 =0 ?"

I'd could help if I could get a 'feel' for what the course is and what level the questioner is at with the work.  But, without a response I cannot do more.  If you're reading this sameer, TALK TO US!.

Bob

hi sameer,

Too many questions at once.  Just started to look at the range question.

But the sine ones are easier so I'll start there.

When you first meet sine and cosine it's in a right angled triangle.  diagram below

sine A = O/H

so when A = zero Opposite = zero, so sinA = zero

If you start with an equilateral triangle (all sides = 2) and cut it down the middle one half is a right angled triangle.

The angles are 30, 60 90 and H= 2, 'O' = 1 so sin 30 = 1/2.

The range question suggests to me that you are now onto the more general definition of sine cosine and tangent which allows any angle not just those in a right angled triangle.  (see second diagram)

More will follow .... just want to check what I've done so far.  Please reply so I know you're ok so far.

Bob

Hi Carisma,

I thought I could do these questions easily but I'm getting an answer in 3 figures (?).

Help me out here.  What answers did you get for a and b?

Bob

hi bobbym,

I agree.  I like helping people with their maths, but, if they're genuinely stuck on homework and wnat to learn more about the topic, then just a straight 'heres the answer' isn't going to do them any good.  They won't be able to make a post when they're doing their exam!

I'd prefer it if someone said: 'Its my homework and I want to get the answer myself but please could someone point me in the right direction.'

It would also be courteous to say thanks afterwards.  Or even some feedback that says whether the help provided actually clarified it for them.  If someone posted back and said 'Im still a bit confused about ......'.  No problem to add more help where it's genuinely needed.

For anyone else reading this, please take note!

Bob

ps.  bobbym, I'm still working on the Cauchy problem.  Thought I had it the other day, but I just went round in a perfect circle and landed back where I'd started.

pps  D'ya think they think we get paid for this?

Hi

There are too many threads muddled up here.  Can someone split them please?

There is a formula for working out the area of any triangle (doesn't require a right angle)

where a, b, c are the lengths of the sides and

But you need to know x first, unless what you are wanting is a formula for the area in terms of x.

sameer mishra: You need to respond to the questions you have been asked about both of the problems you have posted.

Bob

hi again,

to prove tan20.tan30.tan40 = tan10

thus putting (1) and (2) together

hi learn2teach,

I think my response is unchanged.  Afterall, it's what you do that's important; not what the rest of the profession do!

So, to provide a good education, I would recommend you teach them to think.

To help them to pass the tests, proceed as follows.

(i) Get as many old test papers as you can to use as practice tests.

(ii) Give them a test and mark it.

(iii) Based on the 'failed' questions and areas that you identify as causing a problem, make a hints sheet that helps them towards an answer without actually giving the answer.

(iv)  Give the class a limited amount of time to do corrections using your hints.  Circulate to encourage and give additional help if the hint isn't enough.  TARGET: to improve their mark by 15%.

(v) Repeat the process with the next paper.

I have done this for years with SATs pupils (UK age 13/14) and GCSE students (UK age 15/16)

You will find examples of hints sheets on my website www.bundy.demon.co.uk/lessons

These are based on questions that you haven't seen of course but, it'll give you an idea what I mean.  Mostly they are WORD documents so you are welcome to download any you like and extract bits that might be useful to you.  The same goes for any others on the site.  I did these over many years; some are lesson plans and refer to specific text books so will be less useful; but others are there to provide help on topics that might be useful to others.

Now I'm retired, I've got time to sort out these pages and take off the stuff that's not really much help to make room for new stuff by request so any feedback would be welcome.

Bob

hi

3x + 4y + 5z = 12 is the equation of a plain in 3D and the other is the square of the distance from the origin to the plain.  The minimum distance is the length of a line from the origin, that is perpendicular to the plain.

Do you know how to get the vector form for such a line ?

If not, I'll post it.

Bob

Hi Natkirky,

But where is the 'equals' in your equation ?

This may make it easier.

Bob

Hi JaneFairfax,

Thanks for the hide help.  But I've still not fully grasped it.  You can create a box which has a 'title' embedded in it. 

eg. 

but where do I put the hidden content?

Bob