Question 924929
Suppose cos(t)=-1/3 and sin(t)<0 Use appropriate identities to find each of the following?
sec(-1)
sin(-t)
cos(t+5&#960;/3)
sin(2t)
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cos(t)=-1/3
sin(t)<0
reference angle t is in quadrant III where sin<0, cos<0
sin(t)=-&#8730;(1-cos^2(t))=-&#8730;(1-1/9)=-&#8730;(8/9)=-&#8730;8/3
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sec(-1)=1/cos(-1)=1/-0.54&#8776;-1.85
note:(reference angle=1(radian) in quadrant IV where sin<0)
sin(-t)=-sin(t)=-&#8730;8/3
cos(t+5&#960;/3)=cos(t)*cos(5&#960;/3)-sin(t)*sin(5&#960;/3)
=-1/3*1/2-(-&#8730;8/3)*(-&#8730;3/2)=-1/6-&#8730;24/6=-(1+&#8730;24)/6
..
sin(2t)=2*sin(t)*cos(t)=2*-&#8730;8/3*-1/3=2&#8730;8/9