find the exact values( no decimals) of sin u/2, cos u/2, tan u/2, csc u/2, sec u/2 and cot u/2. using the half angle formuals

Question

sin u = -squre root 5/7 , pi< u< 3pi/2

Answer 1

Claire:

I know my x coordinate is -44^(1/2), since (7²-5^(1/2)*2)^(1/2)=44^(1/2)

and when he angle u is in 3rd quadrant the x coordinate is negative.

so cos(u)=-44^(1/2)/7

the half angel will be in 2nd quadrant and cos wil be negative while sin will be positive

formula for cos(u/2) is =/-((1+cos(u))^(1/2))/2)

for your problem cos(u/2)=-((1+(-44^(1/2)/7)^(1/2))/2) important, subtract 44^(1/2)/7

formula for sin(u/2) is =/-((1cos(u))^(1/2))/2)

for your problem sin(u/2)=+((1-(-44^(1/2)/7)^(1/2))/2) important, add 44^(1/2)/7

for tan(u/'2) use tan(u/2)=sin(u/2)/cos(u/2)

for sec(u/2) use sec(u/2)=1/cos(u/20

for csc(u/2) use csc(u/2)=1/sin(u/2)

Answer 2

sin u = -squre root 5/7

=-714/1000=-357/500

μ=-45+58/100=45+29/50

942/100<μ<942/200

471/50 472/100

236/50

118/25