Dooodyo's noob questions

[dooodyo]

Hey guys,

Just have one question how would you find all intercepts for sin 3x =1 for ( -2pie, 2pie) ?

THanks in advance

[luken93]

3x = sin^-1(1)
3x = pi/2
x = pi/6

Then add/subtract period (2pi/3)

x = pi/6 - 4pi/6, pi/6, pi/6 + 4pi/6
 = -3pi/6, pi/6, 5pi/6

[Greatness]

sin(3x)=1 has a reference angle of pi/2
therefore: 3x=pi/2
x=pi/6     -now to get it within the domain. the period is 2pi/3, so add & minus 4pi/6 from pi/6
thus: x= -11/pi, -7pi/6, -pi/2, pi/6, 5pi/6, 3pi/2

[dooodyo]

Oh haha thanks heaps Swarley and Luken

And do you always add or subtract period?

Or sometimes I thought you just add or subtract 2pie from the 1st quad angle? soooo confused 

[Greatness]

It depends what you want to do. If you were to find solutions in a restricted domain then find the first 2 solutions, then you can add, subtract the period from/to the solutions. It just depends on what thte domain is.
If you have 23pi/4 but the questoin wants it in [0,2pi] then 13pi/6 - 2pi = pi/6.

[dooodyo]

Wait so does that mean you add 2pie or add the period each time?

[Greatness]

oh sry for the confusion. When you're finding solutions you add the period. However if you want to find an equvialent angle then you add/subtract multiples of 2pi.
I thinks that right

[dooodyo]

Hey guys,

I have another noob question any help would be appreciated.

How would you find the general solution to sqrt(3)tan(pi/6-3x)-1=0 ?

why is it (pi x n)/3 and not (-pi x n)/3 ?

[brightsky]

They are the same, since n is any integer.

[Aurelian]

Hey guys,

I have another noob question any help would be appreciated.

How would you find the general solution to sqrt(3)tan(pi/6-3x)-1=0 ?

why is it (pi x n)/3 and not (-pi x n)/3 ?

They are the same, since n is any integer.

Provided your solution is followed by "n E Z"

You could, however, say +/- both those options, but you'd need to say "n E N U O"

[brightsky]

You could, however, say +/- both those options, but you'd need to say "n E N U O"

There are infinite many ways to write the 'general solution'. I'd say just write one, with n E Z at the end as Aurelian said. I'm pretty sure all the 'variations' would be accepted, as all of them are technically correct.

[Aurelian]

Yeah, I'd stick to the n E Z variation like brightsky said - less room for silly mistakes.

Also, this might be of help;

http://vce.atarnotes.com/forum/index.php/topic,35962.msg382191.html#msg382191

[dooodyo]

wait does " n E N U O " mean element of natural no.s union 0 ?

[Aurelian]

wait does " n E N U O " mean element of natural no.s union 0 ?

Yep I'd have used latex but I don't know how haha sorry

[dooodyo]

Thanks heaps