Half Angle Identities

[bluewater]

sin(?/2)=±?(1/2)(1-cos?)
cos(?/2)=±?(1/2)(1+cos?)
tan(?/2)=(1-cos?)/sin?

1.tan(7pi/8)
= (7pi/4)/2
={1-(?2/2)}/(?2/2)
={(2/2)-(?2/2)}/(?2/2)

2.cos 165°

3.cos(15pi/8)

4.sin(-pi/8)

5.tan -67.5°

Thanks!

 

[DrMike]

sin(?/2)=±?(1/2)(1-cos?)
cos(?/2)=±?(1/2)(1+cos?)
tan(?/2)=(1-cos?)/sin?

1.tan(7pi/8)
= (7pi/4)/2
={1-(?2/2)}/(?2/2)
={(2/2)-(?2/2)}/(?2/2)

2.cos 165°

3.cos(15pi/8)

4.sin(-pi/8)

5.tan -67.5°

Thanks!

What, exactly, are you asking?

 

[bluewater]

help finishing #1 and help starting the others

 

[Deleted member 4993]

sin(?/2)=±?(1/2)(1-cos?)
cos(?/2)=±?(1/2)(1+cos?)
tan(?/2)=(1-cos?)/sin?

1.tan(7pi/8)
= (7pi/4)/2 <<< What is that?

tan(7?/8) = tan (? - ?/8) = - tan(?/8) = - tan ((?/4)/2) = -(1 - 1/?2)/(1/?2) = - (?2 - 1)

={1-(?2/2)}/(?2/2)
={(2/2)-(?2/2)}/(?2/2)

2.cos 165° = cos (180° - 15°) = - cos (15°) = - cos (30°/2) ... and continue...

3.cos(15pi/8) = cos (2? - ?/8) = cos ((?/4)/2)... and continue

4.sin(-pi/8) ... similar to above...

5.tan (-67.5°) = tan (-(?/2 - 22.5°)) = - tan (?/2 - 22.5°) = - cot(22.5°) = - 1/tan(22.5°) = - 1/tan((45°)/2) ... continue..

Thanks!