13 replies to this topic

[gillian1989]

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

[Mr H]

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?

[gillian1989]

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

[Mr H]

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

[gillian1989]

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

[Mr H]

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

[gillian1989]

no problem, and thanks for all you help!

[Mr H]

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!

[Steve]

I got tan(x) also.

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



If you collect together like terms and simplify, you should get .

[Mr H]

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?

[gillian1989]

ok thank you both for all you help!

[Steve]

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:

and

CODE

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

gives:

[Mr H]

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:


Very cool! Thanks again!!

[Steve]

No problem