SOLUTION: given cot (theta) = 12/5 and 180<(theta)<270, what is cos (theta/2)?

Question 903306: given cot (theta) = 12/5 and 180<(theta)<270, what is cos (theta/2)?

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
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)=-√((1+cosx)/2)=-√((1-12/13)/2)=-√((1/13)/2)=-√(1/26)=-1/√26
Check:
cos x=-12/13 (in Q3)
x=202.6198˚
x/2=101.3099˚
cos(x/2)≈cos(101.3099)≈-0.1961...
exact value as calculated=-1/√26≈-0.1961...
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