where does this come from???..again

lorr3

another wee problem with maths...

could anyone tell me why 4 b ii Paper 2 works out like it does....
am stumped and it seems simple
http://www.examinations.ie/archive/markingschemes/2006/LC003ALPO00EV.pdf
thanks:)

Craguls

It's because sin minus sin is 2cos it always help to have the tables open when doing these!

lorr3

oh sorrry no i get that part but i cant get how 2x+30 = ... and x+30=....

Well, firstly they've used an identity in reverse:

sin(A+B)-sin(A-B) = 2cosAsinB

Now, since the 2cos(2x+30)sin(x+30) = 0, we know that one of it's factors has to equal 0. This is logical if you think about it: if two things multiplied together equal 0, then one of them at least must equal 0. So next we just seperate both halves of the equation and let it equal 0.

Each component [cos(2x+30) and sin(x+30)] are let equal 0. Now, you know that cosine only ever equals zero for 90 degrees, but, it repeats itself with a period of 180 degrees. So you let the 2x+30 = 90, then 270, then 450 etc. etc. (they're just 90 + 180, then plus 180 etc.). The same goes for the sine component, but we know that sine only ever equals 0 for 180 degrees, and it has a period of 180, so it will equal 0 at 360, 540 etc. So we let x+30 equal the angle of 180, 360 etc. Then you just solve the equations, e.g:

2x+30 = 90; 2x = 60; x = 30.

You'll get a solution set of a good few angles, but, I'm sure the question will have specified that the angle will be between 0 and 360 or something. So you just include those angles that fit the bill.

lorr3

thanks jam get it now. havin the 2x thing made me go???? silly me.:) thank you