Question 549871
If sin x =12/13, where pi/2 <= x <= pi, determine:
a) sin (x/2)
b) sec (x/2)
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You are working with a reference angle in quadrant II where sin>0 and cos<0
sin x=12/13 (given)
cosx=-5/13
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a) Using half-angle formula for sin
sin x/2=&#8730;[(1-cosx)/2]=&#8730;[(1+5/13)/2]=&#8730;[(18/13)/2]=&#8730;[(18/26]
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b) Using half-angle formula for cos then taking the reciprocal
cos x/2=-&#8730;[(1-cosx)/2]=-&#8730;[(1-5/13)/2]=-&#8730;[(8/13)/2]=-&#8730;[(8/26]
sec x/2=1/(cos x/2)=-&#8730;(26/8)