Melody

2cos^2 theta + sin theta-2=0

$$2(1-sin^2\theta) +sin\theta-2=0\\\\
2-2sin^2\theta +sin\theta-2=0\\\\
-2sin^2\theta +sin\theta=0\\\\
sin\theta(-2sin\theta+1)=0\\\\
sin\theta=0\qquad or\qquad -2sin\theta+1=0\\\\
\theta=0,\pi,2\pi,...\;\; or\;\;sin\theta=1/2\\\\
\theta=0,\pi,2\pi,...\;\; or\;\;\pi/6,\;\; 5\pi/6\\\\
so\; for\; the \;domain\; [0,2\pi)\\\\
\theta=0,\;\frac{\pi}{6}, \;\frac{5\pi}{6}\;and\;\pi\\\\$$

you beat me Chris :(

I'm not letting you have points for this Dragon!

Look here

I've just added the wiki referrnce address to the LaTex thread.

Thanks Ninja.

Thanks 15x3.  

I am assuming that the service charge of $1294.64 is paid up front and seperate to the rest of the loan.

I have made a few assumptions here.     

A=15360

r=0.0958/2 = 0.0479

n=8*2=16

$$\begin{array}{rll}
15360&=&P\left[\frac{1-(1.0479)^{-16}}{0.0479}\right]\\\\
15360\div \left[\frac{1-(1.0479)^{-16}}{0.0479}\right] &=&P\\\\




\end{array}$$

$${\frac{{\mathtt{15\,360}}}{\left({\frac{\left({\mathtt{1}}{\mathtt{\,-\,}}{{\mathtt{1.047\: \!9}}}^{-{\mathtt{16}}}\right)}{{\mathtt{0.047\: \!9}}}}\right)}} = {\mathtt{1\,396.160\: \!459\: \!256\: \!217\: \!018\: \!8}}$$

So Sam will pay a total of 1396.16*16 = $22338.56

Interest charged = 22338.56-15360 = $6978.56  

Total finance charge = 6978.56+1294.64 = $8273.20

% wanted if I understand the terms correctly is  1294.64/8273.20*100

$${\frac{{\mathtt{1\,294.64}}}{{\mathtt{8\,273.2}}}}{\mathtt{\,\times\,}}{\mathtt{100}} = {\mathtt{15.648\: \!600\: \!299\: \!763\: \!090\: \!5}}$$

15.65%

Ok Chris - I will let you have the last word.  The term is a little ambiguous.

Fri 2/8/14  Some of these would make really nice additions to your 'Great questions to learn from' thread Ninja. 

I'll try and categorise them for you.   

 Working with logatithms. Hard one.

@@ End of Day Wrap :   Thurs 31/7/14     Sydney, Australia     Time 1:00am   (Really Friday morning)   ♬

Hi all,        ♫♪

Our great answers were today provided  by CPhill, Alan, NinjaDevo, Heureka, DragonSlayer554 and AzizHusain.

My thanks to each of you.  

NinjaDevo has been working on this great thread for everyone and now it is finished.  It is a thread of great answers to learn from - just like the title suggests.  This should be great reference material for askers and answerers but it is intended more for the askers.  NinjaDevo has presented it beautifully, it will be constantly added to.  Maybe now much fewer of our wonderful questions and answers will be lost.  If you would like a post added please private message the address of the post to Ninja.  This is Ninja's thread and he will have the final say as  to which threads are included and which are not but he can not find all the good ones himself.  He will need help for this.  Thank you Ninja.  I am very grateful to you for taking care of all our reference material.

Oh, "Great answers to learn from" and "Reference Material" are both Sticky Topics  

Hey Stu, if you are felling generous you could give Alan some thumbs up.