Question 499494
Use the given information to find each value.
sint=(-12/13) &#960; < t < 3&#960;/2 
(a) cos 2t 
(b) sin 2t 
(c) cos(t/2) 
(d) sin(t/2) 
**
sint=(-12/13)
You are working with 5-12-13 right triangle in quadrant III where sin and cos are<0
cost=(-5/13)
..
(a) cos 2t=cos^2t-sin^2t=(-5/13)^2-(-12/13)^2=0.1479-0.8521=-0.7042
(b) sin 2t=2sintcost=2(-12/13)(-5/13)=0.7101 
(c) cos(t/2)=±&#8730;((1+cost)/2)=-&#8730;((1-5/13)/2)=-&#8730;0.3077=-0.5547 (choose negative root because t/2 is in quadrant II where cos is <0
(d) sin(t/2)=±&#8730;((1-cost)/2)=&#8730;((1+5/13)/2)=&#8730;0.6923=0.8320 (choose positive root because t/2 is in quadrant II where sin is >0