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Gradient of a line


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#1 gillian1989

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Posted 17 April 2006 - 07:59 PM

P is the point with coordinates (sin(x+30), cos(x-30) and Q has coordinates (sin(x-30), cos(x+30) find in its simplest form and expression of the gradient of the line PQ

iv tried it heaps of times bt i just end up with lots of stuff n get cofused! please help! x

#2 Mr H

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Posted 17 April 2006 - 08:50 PM

I haven't time to work right through it all myself just now but is this what you have tried so far?

stick all coords into gadient formula,
expand each trig expression using the addition formulae (be very careful to keep the y1, x1 bits in brackets as the minus will affect signs),
simplify using exact values,
simplify trig parts,
simplify further if required.

Which bit is causing you the most bother?

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#3 gillian1989

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Posted 17 April 2006 - 08:57 PM

well iv done the exact values bit and i just end up with a bunch of fractions and some sinx n cosx's and i cant seem to simplify it

#4 Mr H

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Posted 17 April 2006 - 09:05 PM

Write down what you have as your last line for me and I'll go and work through the sum in the meantime.

H tends 2 infinity

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#5 gillian1989

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Posted 17 April 2006 - 09:13 PM

(root3/2 cosx+ 0.5sinx) - (root3/2 cox -0.5 sinx) / (sinxcosx+root3/4) - (sinxcosx +root3/4)

#6 Mr H

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Posted 17 April 2006 - 09:18 PM

Right, back in a minute, somethings come up at home.

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#7 gillian1989

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Posted 17 April 2006 - 09:20 PM

no problem, and thanks for all you help!

#8 Mr H

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Posted 17 April 2006 - 09:23 PM

I've done it very quickly and I get it to all simplify down to tanx after two lines. But I'll have a quick check in case I made a mistake!

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#9 Steve

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Posted 17 April 2006 - 09:29 PM

I got tan(x) also.

The thing to watch here is signs when you use the trig expansions. I get to:



\begin{align*}m&=\frac{\cos x\cos 30-\sin{x}\sin30-\cos{x}\cos{30}-\sin{x}\sin30}{\sin{x}\cos30-\cos{x}\sin30-\sin{x}\cos30-\cos{x}\sin30}\end{align*}

If you collect together like terms and simplify, you should get m=\tan{x}.
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#10 Mr H

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Posted 17 April 2006 - 09:32 PM

Same answer again.

After expanding all four expressions you should find that two cancel on both top and bottom lines to leave you with -2sinxsin30 over -2cosxsin30. You even don't need to use exact values as the -2's and sin30's cancel top & bottm to leave sinx/cosx = tanx.

Thanks Steve! I need to find out how to do the LaTeX stuff! Any tips?

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#11 gillian1989

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Posted 17 April 2006 - 09:34 PM

ok thank you both for all you help!

#12 Steve

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Posted 17 April 2006 - 09:43 PM

You can get a free program from the makers of MathType, called TeXaide. You can use it like MathType but you can copy the maths and it pastes as LaTeX code - it really helps you to get used to the code. (You don't need to enter your e-mail address to download the program.)

Also, MathType can do the same sort of thing (if you have that). You have to go to Preferences > Translators... then choose "Translation to other language", any TeX format should work.

PS - you don't want to enter comments into the forum (lines starting with %), and you use

CODE
[tex][/tex]

tags around the maths you want to be displayed inline instead of

CODE
\[  \]

and use

CODE
[display][/display]

to get maths you want to be in a display style. E.g.:

CODE
[tex]f(x)=1+\frac{1}{x}[/tex]

gives: f(x)=1+\frac{1}{x}

and

CODE
[display]f(x)=1+\frac{1}{x}[/display]

gives: 

\begin{align*}f(x)=1+\frac{1}{x}\end{align*}
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#13 Mr H

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Posted 17 April 2006 - 09:58 PM

That's great Steve, thanks very much for that!
I generally stick to Equation Editor as its pretty standard among Maths teachers for making worksheets, etc.

I'm away to give that a go.

Cheers!


Edit:


\begin{align*}\int\limits_1^4 {\left( {x^2  + \frac{x}{2}} \right)dx} \end{align*}

Very cool! Thanks again!! biggrin.gif

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#14 Steve

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Posted 17 April 2006 - 10:07 PM

No problem smile.gif
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