Question 668478
<font face="Times New Roman" size="+2">


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \tan{\theta}\ =\ \frac{\sin\theta}{\cos\theta}\ =\ \frac{-\sqrt{7}}{2}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\sin\theta\ =\ -\sqrt{7}\cos\theta]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4\sin^2\theta\ =\ 7\cos^2\theta]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4\sin^2\theta\ =\ 7\left(1\ -\ \sin^2\theta\right)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 11\sin^2\theta\ =\ 7]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sin\theta\ =\ \pm\frac{-\sqrt{77}}{11}]


But secant is the reciprocal of cosine, so if secant is positive, cosine is positive.  Tangent is sine over cosine, so if cosine is positive sine is negative when tangent is negative.


Therefore


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sin\theta\ =\ -\frac{-\sqrt{77}}{11}]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
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>