Ken's specialist question thread!

[kensan]

So I hope this is the right thing to do and start my own question thread >.<

So the first topic we have been studying is circular functions and I am having trouble with this question. It has to do with double or half angle formula. I know I've made a mistake somewhere, or maybe gone off on a completely wrong tangent
Would be great if someone could help!
Also do I need to do that LaTex business?

[moekamo]

you don't simply divide by tan(x) between your 5th and 6th lines, what if tan(x)=0???
you have to put everything on one side of the equation and factor out tan(x) and let each factor=0 then solve. the part with taking the square root of a negative just mean that factor never equals 0 so you can ignore it when solving for x.

you should get x=0, pi, 2pi

[trinh]

I think you went wrong in line 6 of your working out, where you divided both sides by ; the problem in doing this is that you haven't considered the possibility of , so you risk 'losing' solution(s).

So from your 5th line of working, expand everything out, to get:


Then use null factor law to solve:

and
- this has no solutions btw

Edit: Beaten xD

[kensan]

Thanks guys! I get it now, relief 

[kensan]

Ok so I'm having problems with this question

cos[2cos^-1(5/13)]

I've written 2cosx=(5/13)       
                  cosx=(5/26)

Not too sure where to go from there.

PS, sorry I'm still sorting out the Latex business 

[kamil9876]

You made a mistake, but I can't point all of it out since I don't see your reasoning(what is x supposed to be?). For starters, surely is false (most of the time). Try to use the double angle formula by putting in

[kensan]

I'm just using the method that the example used haha
Say,  tan(Arccos(1/3)
The book then says to make   cosx=(1/3)    which is  secx=3
so      tan²x+1=sec²x
          tan²x=9-1=8
          tanx= two root two

That's why I made the x

Also, sorry, where did I make cos(2x)=2cos(x)?

Oh yeah do do I need to download a program to use latex?

[pi]

I'm just using the method that the example used haha
Say,  tan(Arccos(1/3))

I'd find drawing a triangle to be much easier for this problem.

Oh yeah do do I need to download a program to use latex?

No, just click the button when you post and type using LaTeX. A short guide can be found here: LaTeX typeset in Maths boards

[monkeywantsabanana]

Use this: http://www.codecogs.com/latex/eqneditor.php

[kamil9876]

Also, sorry, where did I make cos(2x)=2cos(x)?

Sorry, yeah you didn't make that mistake, I must've read your post too quickly.

I've written 2cosx=(5/13)       
                  cosx=(5/26)

For some reason I read (5/13) as cos(5/13), the unnecessary brackets must've put me off haha

[kensan]

Awesome thanks for latex info guys

[nina_rox]

Hi, I have a quick question. Does it matter if you label the points anti-clockwise or clockwise? For example if there is a rhombus OABC, how would you label it?

[aznxD]

Doesn't matter. As long long as it's in the order OABC.

[nina_rox]

Doesn't matter. As long long as it's in the order OABC.

Thank you!

[kensan]

Having trouble with this

I've done a(i),
Answer to that was    ( being degrees)
But not sure how to find the maximum volume from that. I know with quadratics last year we used derivative=0 to find stationary points etc, but I'm lost on how to do it with this.
And part b I'm not sure what to do.
Thanks!