Functions Involving Double Angles

[nycmathguy]

Section 5.5

 

[MathLover1]

given:
cos(u)=-4/5, pi/2<u<pi
we know that cos(u)=-4/5-> adj=4, hyp=5
then
opp=sqrt(5^2-4^2)
opp=sqrt(25-16)
opp=sqrt(9)
opp=3

sin(u)=3/5

sin(2u) = 2sin(u) cos(u)
sin(2u) = 2(3/5)(-4/5)
sin(2u) =-24/25

cos(2u) =cos^2(u) - sin^2(u)
cos(2u) =(-4/5)^2 - (3/5)^2
cos(2u) =7/25

tan(2u)=sin(2u)/cos(2u)
tan(2u)=(-24/25)/(7/25)
tan(2u)=-24/7

 

[nycmathguy]

given:
cos(u)=-4/5, pi/2<u<pi
we know that cos(u)=-4/5-> adj=4, hyp=5
then
opp=sqrt(5^2-4^2)
opp=sqrt(25-16)
opp=sqrt(9)
opp=3

sin(u)=3/5

sin(2u) = 2sin(u) cos(u)
sin(2u) = 2(3/5)(-4/5)
sin(2u) =-24/25

cos(2u) =cos^2(u) - sin^2(u)
cos(2u) =(-4/5)^2 - (3/5)^2
cos(2u) =7/25

tan(2u)=sin(2u)/cos(2u)
tan(2u)=(-24/25)/(7/25)
tan(2u)=-24/7

Wow! I totally messed up here. I will try 34 on my own.