Half-Angle Formulas...4

[nycmathguy]

Section 5.5

 

[MathLover1]

sin(u)=5/13-> opp=5, hyp=13=> adj=sqrt(13^2-5^2)=12
cos(u)=12/13

sin(u/2)=sqrt((1-cos(u))/2)
sin(u/2)=sqrt((1-12/13)/2)
sin(u/2)=sqrt((1/13)/2)
sin(u/2)=sqrt((1/26)
sin(u/2)=sqrt(26)/26

 

[nycmathguy]

sin(u)=5/13-> opp=5, hyp=13=> adj=sqrt(13^2-5^2)=12
cos(u)=12/13

sin(u/2)=sqrt((1-cos(u))/2)
sin(u/2)=sqrt((1-12/13)/2)
sin(u/2)=sqrt((1/13)/2)
sin(u/2)=sqrt((1/26)
sin(u/2)=sqrt(26)/26

Where did I go wrong?
Can you point out my error?

 

[MathLover1]

while doing sin(u/2), you got a line

=sqrt(1/26) which is correct, then your next line is

=sqrt(1)/sqrt(13) instead sqrt(1)/sqrt(26)

 

[nycmathguy]

while doing sin(u/2), you got a line

=sqrt(1/26) which is correct, then your next line is

=sqrt(1)/sqrt(13) instead sqrt(1)/sqrt(26)

Making errors leads to learning.

 

[nycmathguy]

while doing sin(u/2), you got a line

=sqrt(1/26) which is correct, then your next line is

=sqrt(1)/sqrt(13) instead sqrt(1)/sqrt(26)

 

[MathLover1]

correct

 

[nycmathguy]

correct

Finally got it right.