<PRE><B>Question 875547</B>
Find the exact value
Given that sin &amp;#1256; = -4/5 with &amp;#1256; in quadrant IV, find tan 2&amp;#1256; 
***
you are working with a (3-4-5) reference right triangle in quadrant IV
sin &amp;#1256;=-4/5 (given)
cos &amp;#1256;=3/5
sin 2&amp;#1256;=2sin&amp;#1256;cos&amp;#1256;=2*-4/5*3/5=-24/25
cos 2&amp;#1256;=cos^2&amp;#1256;-sin^2&amp;#1256;=9/25-16/25=-7/25
tan 2&amp;#1256;-sin 2&amp;#1256;/cos 2&amp;#1256;=24/7
..
Check:
sin &amp;#1256;=-4/5
&amp;#1256;&amp;#8776;306.87&amp;#730;
2&amp;#1256;&amp;#8776;613.74&amp;#730;
tan 2&amp;#1256;&amp;#8776;3.4286…
exact value as calculated=24/7&amp;#8776;3.4287…</PRE>