sin(A)=(4/5), ((pi/2)<A<pi), tan(B)=(-12/5), ((3pi/2)<B<2pi)

sin((1/2)A)?

cos((1/2)A)?

we find the value of A, from sin(A)=(4/5) we have;

A=sin^(-1)(4/5)

A=sin^(-1)(0.8)= 53.13

for A between 90 and 180 then A= 90+53.13= 143.13

or A=180-53.13= 126.87

for A=126.87 the sin((1/2)A)=sin 63.435= 0.89443

cos ((1/2)A)=cos 63.435= 0.4472

answers could differ slightly due to rounding-off

Do you know how to solve it in fractions rather than decimals?

okay, the angles are irrational values. but A can be written as (53*pi)/180

for pi/2<A<pi then A=pi + (53*pi)/180

A=(233*pi)/180

sin ((1/2)*A)=sin {(233*pi)/360}=9/10

cos((1/2)*A)=cos{(233*pi)/360}=1/2

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