I am still having trouble with these, maybe you could explain what I am doing wrong, here are a few I have been working on.

find tan angle

tan angle in QII, sec angle=-4/sqrt(5)

tan 2 angle in QI, cos 2 angle=3/5

tan 2 angle in QI, csc 2 angle=4/3

tan angle/2 in QII, Sec angle/2=-4

sin angle/2=1/3

here is what I did

sec angle=-4/sqrt(5), sec=1/cos

tan^2 angle+1=(-4/sqrt(5))^2

tan^2 angle +1= 16/5

since sec is neg is QII, tan=-sqrt(11/5)

cos2 angle=3/5, cos is pos in QI

cos^2 angle=1-sin^2 angle

(3/5)^2=1-sin^2 angle

sin angle= 4/5

tan=sin angle/con angle= 4/5/3/5= 4/3

tan= 2(4/3)= 8/3

tan2 angle in QI, csc2 angle= 4/3, csc is pos in QI

csc angle = 1/sin angle

cos^2 angle=1-1/4/3

cos^2= 9/4, cos= 3/4

csc2 angle, cos angle=9/4

tan^2 angle +1=(1/9/4)^2

tan^2 angle +1= 16/81

I can see this is going badly.

tan angle/2 in QII, sec angle/2=-4, sec in QII is neg

sec= 1/cos angle

tan^2 angle+1=(-8)^2

tan^2 angle=63

tan=sqrt(63)

tan angle/2 in QII= -6sqrt(7)

sin angle/2= 1/3

+-sqrt(1-cos a/2)= +-sqrt(1-1/3/2)= +-sqrt(1/3)

Could you please show me what I am doing wrong. I have been working on this for a few hours and I think a thirty minute break to clear my head might do some good before I start doing some more problems. I would appreciate all and any suggestions you can give because I reall want to understand these identities.

Thank You very much!!!!

Keith Stevens