Simplifying Trig Identities

Lesson:
Half Angle Identities-
sin u/2= ±√1-(cos u/2)
cos u/2=±√1+(cos u/2)
tan u/2= 1-(cos u/ sin u) = (sin u/ 1+cos u)
Plug in the numbers and then solve.

Here is a pretty difficult one
1.Find the exact value of the half angle of sin(π/12)
sin(a/2) = ± √(1-cos/2)/2
sin a/2= π/12
a=π/6
sin ((π/6)/2) = √(1-cos π/6)/2
=√(1-√3/2)/2
= √(2-√3)/2
=√(2-√3)/4= √(2-√3)/2

Now let's go a step further
2. Find the cos (t) = -7/9 where π < t < 3π/2
Divide everything by 2 to get t/2 in the middle
π/2 <t/2 < 3π/4
sin (t/2) = ± (√1-cos (-7/9) / 2 = √(16/9)/2 = √8/9 = √8/3