Question 882977
If tan A=5/12 and A is in the third quadrant find {{{cos2A}}} and {{{cos (A/2)}}}
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tanA=5/12 (working with a (5-12-13) reference right triangle in quadrant III in which sin<0, cos<0, tan>0
sinA=-5/13
cosA=-12/13
cos 2A=cos^2A-sin^2A
cos 2A=144/169-25/169=119/169
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{{{cos(A/2)=sqrt((1+cos(A))/2)=sqrt((1-(12/13))/2)=sqrt((1/13)/2)=sqrt(1/26)=sqrt(26)/26}}}