trig
posted by Spy[c] on .
Solving Trig Functions: How Do You Solve For Sin 7.5 Using HalfAngle and DoubleAngle Identities?

Formulas to remember:
sin(2a)=2sin(a)cos(a)
cos(2a)=cos²(a)sin²(a)
From the second equation, replace a by a/2 and 2a by a to get
cos(a)=cos²(a/2)sin²(a/2)
=2cos²(a/2)1 ...(1)
=12sin²(a/2) ...(2)
From (1) we get
cos²(a/2)=(1/2)(1+cos(a))
From (2) we get
sin²(a/2)=(1/2)(1cos(a))
So
sin(7.5)
=√((1/2)(1cos(15))
=√((1/2)(1√((1/2)(1+cos(30))))
=√((1/2)(1√((1/2)(1+√(3)/2)))
=0.13... 
dersagt