Use the given information to find the exact value of sin alp

Use the given information to find the exact value of sin alpha/2, cos alpha/2, and tan alpha/2. tan alpha = 15/8, 180degree

Solution

180<a<270

=>90<a/2<135

given tana=15/8

cosa=-8/(15²+8²)

cosa=-8/17

a) sin(a/2) =[(1-cosa)/2]

sin(a/2) =[(1-(-8/17))/2]

sin(a/2) =(25/34)

sin(a/2) =5/34

b) cos(a/2) =-[(1+cosa)/2]

cos(a/2) =-[(1+(-8/17))/2]

cos(a/2) =-(9/34)

cos(a/2) =-3/34

c)tan(a/2)=sin(a/2)/cos(a/2)

tan(a/2)=((25/34))/(-(9/34))

tan(a/2)=-(25/9)

tan(a/2)=-5/3