Question 1163852
<font face="Times New Roman" size="+2">


Use the Cosine of the Difference of Two Angles Identity:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos\(\alpha\,-\,\beta\)\ =\ \cos\alpha\cos\beta\ +\ \sin\alpha\sin\beta]


To do this you will have to calculate *[tex \Large \cos u] and *[tex \Large \sin v] given *[tex \Large \cos v] and *[tex \Large \sin u].  The process in general is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sin\varphi\ =\ x]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sin^2\varphi\ =\ x^2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \1\ -\ \cos^2\varphi\ =\ x^2\ \ ](Pythagorean Identity)


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos^2\varphi\ =\ 1\ -\ x^2]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos\varphi\ =\ \pm\sqrt{1\,-\,x^2}\ \ ] (Choose sign based on quadrant)


Finding cosine given sine is the same process.

																
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  
								
{{n}\choose{r}}
</font>