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

## Gradient of a line With trig coordinates

### Mr H

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 y

simplify using exact values,

simplify trig parts,

simplify further if required.

Which bit is causing you the most bother?

stick all coords into gadient formula,

expand each trig expression using the addition formulae (be very careful to keep the y

_{1}, x_{1}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

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

### gillian1989

Posted 17 April 2006 - 09:13 PM

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

### Mr H

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?

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?

### Steve

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

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

and use

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

gives:

and

gives:

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: