Question 903306
given cot (theta) = 12/5 and 180<(theta)<270, what is cos (theta/2)?
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you are working with a 5-12-13 reference right triangle in quadrant III in which cos<0
Use x for theta
cos x=-12/13
cos(x/2)=-&#8730;((1+cosx)/2)=-&#8730;((1-12/13)/2)=-&#8730;((1/13)/2)=-&#8730;(1/26)=-1/&#8730;26
Check:
cos x=-12/13 (in Q3)
x=202.6198&#730;
x/2=101.3099&#730;
cos(x/2)&#8776;cos(101.3099)&#8776;-0.1961...
exact value as calculated=-1/&#8730;26&#8776;-0.1961...