Question 772225
<font face="Times New Roman" size="+2">


*[tex \LARGE u] is in QI, so both sin and cos are positive.


*[tex \LARGE \sin(u)\ =\ \frac{5}{13}]


*[tex \LARGE \sin^2(u)\ =\ \frac{25}{169}]


*[tex \LARGE 1\ -\ \cos^2(u)\ =\ \frac{25}{169}]


*[tex \LARGE \cos^2(u)\ =\ \frac{144}{169}]


*[tex \LARGE \cos(u)\ =\ \pm\frac{12}{13}]


Discard negative because of QI.


*[tex \LARGE \cos(u)\ =\ \frac{12}{13}]


Use the same technique to find *[tex \LARGE \sin(v)] based on the value of *[tex \LARGE \cos(v)]


*[tex \LARGE v] is in QII, so *[tex \LARGE \sin(v)\ >\ 0]


Once you have the values for the 4 functions, use those values in the formula for the sine of the difference:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sin\left(\theta\ -\ \varphi\right)\ =\ \sin\theta\cos\varphi\ -\ \cos\theta\sin\varphi]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
<div style="text-align:center"><a href="http://outcampaign.org/" target="_blank"><img src="http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png" border="0" alt="The Out Campaign: Scarlet Letter of Atheism" width="143" height="122" /></a></div>
</font>