BEC'S methods questions

[Mao]

and you should be fine from here

[bec]

thanks, nicely explained!

i have more.....
Find the general solutions to the following equations. Give exact answers:
a)
b)

[dcc]

Question A:





Dividing through by cos(x):





Now we remember all our solutions to tan(x) = 1:



These seem to be following a pattern, so we can say:



Question B:





Dividing through by



Which we can generalise with:



remember, both of these go in the negative direction as well

[bec]

thanks dcc..

one question though, with (a) in the one you just answered and also the question mao answered, why is it ok to divide both sides by cos(x)?
What if cos(x) = 0, wouldn't that be undefined? Or does that just sort itself out when we end up with the list of solutions for x, which don't include pi, pi/2 etc?

[dcc]

ACTUALLY



For this relation to be true, neither of them can be zero, because if one is zero then the other must be zero, and we know that cannot equal zero at the same time as

[AppleXY]

indeed. sin[0] = 0 but cos[0] = 1

[bec]

righhht. well that makes sense!

[bec]

Solve for x:


I thought the best way would be to factorise/solve by nfl - am I right?
If so, is there a more effective way of factorising this than trying P(1), P(2) etc until one = 0?
thanks

[Collin Li]

There might be, but they are special cases where you have to recognise it fits into some special form. I can't spot one, nor does it look like there could be one (the numbers aren't very yummy), so I'll just tell you that works well

It doesn't take that long if you use a shorter form of long division. I use synthetic division. You know that is a factor so you just write down:



Now, fill in the right bracket systematically, working from the highest power of down to the constant term, while also keeping in mind the extra term being produced. I'm not actually sure if you wanted an explanation of this, so I'm not going to explain further unless you ask me to!



Still can't see any nice way to factorise this, so use the guessing game for the last time, before breaking it into a quadratic. Hint:

[bec]

what do you think the chances would be that i'd have to work something like this out in a non-calc question?

[ed_saifa]

low chance

[Glockmeister]

I would say that it is possible to get a 3rd degree polynomial though

[Collin Li]

I would say that it is possible to get a 3rd degree polynomial though

I agree. There is a low chance of a quartic, because it tests the same technique twice (as you can see, you need to guess factors twice).

[Glockmeister]

And for the tech-free exams, they are looking at whether you know how to use the various techniques and formulae that you will learn throughout the year. I remember a chem teacher tell me something along the lines of "examiners only have 7 minutes to completely go through your exam paper." If that were true, they would not want to go about correcting a solution of a 4th degree polynomial.

[droodles]

YES COBLIN BROUGHT UP SYNTHETIC DIVISION