SOLUTION: Derive the half angle formula for sin( u/2 ) by following the steps below. (a) Use the sum angle formula to write cos(2x) in terms of powers of sin(x) and cos(x) . (b) Use a tri

Algebra ->  Trigonometry-basics -> SOLUTION: Derive the half angle formula for sin( u/2 ) by following the steps below. (a) Use the sum angle formula to write cos(2x) in terms of powers of sin(x) and cos(x) . (b) Use a tri      Log On


   

Question 431469: Derive the half angle formula for sin( u/2 ) by following the steps below.
(a) Use the sum angle formula to write cos(2x) in terms of powers of sin(x)
and cos(x) .
(b) Use a trig identity to rewrite cos(2x) in terms of just powers of sin(x):
(c) Solve the formula in part (b) in terms of sin(x), and not a power of
sin(x).
(d) Substitute x = u/2 into the formula in part (c).
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!


cos%282x%29+-+1+=+-2sin%5E2%28x%29

sin%5E2%28x%29+=+%281+-+cos%282x%29%29%2F2

sin%28x%29+=+sqrt%28%281+-+cos%282x%29%29%2F2%29

Replacing x with u/2,

sin%28u%2F2%29+=+sqrt%28%281+-+cos%28u%29%29%2F2%29 (however you must be careful what quadrant u and u/2 are in, because it could be positive or negative).