54 A For the following assume that all the given angles are

5.4

For the following, assume that all the given angles are in simplest form, so that if A is in QIV you may assume that 270°

sin(A/2)= +-sqrt(1-cosA)/2

Cos A=1/2

therefore sin(A/2)= +-sqrt(1-1/2)/2

sin(A/2)=+- sqrt 1/4

sin(A/2)=+-1/2

And in fourth quadrant sin A is negative,therefore sin(A/2) is negative too

Hence the answer is -1/2

sin A=-4/5

On using pythagoras theorem and trigonometric ratio formula we get

cos A=-3/5

cos(A/2)= +-sqrt(1+cosA)/2

cos(A/2)= +-sqrt(1-3/5)/2

cos(A/2)=+- sqrt 1/5

And in third quadrant cos A is negative,therefore cos (A/2)is negative too

Hence the answer is -sqrt1/5