Posted by Nikki on Sunday, July 15, 2012 at 5:48pm.
sin (x/2 ) = + sqrt([1-cos x]/2) if x/2 in q 1 or 2 thus if 0 < x < 2 pi
sin^2 (x/2) = [1-cos x]/2
so
cos^2 x = [1 - cos x]/2
2 cos^2 x = 1 - cos x
2 cos^2 x + cos x = 1
let z = cos x
2 z^2 + z -1 = 0
(2 z - 1)(z +1) = 0
z = cos x = 1/2
or cos x = -1
x = 60 deg (pi/3) or -60 deg (5 pi/3)
or x = 180 deg (pi)
Related Questions
Trigonometry - Use the half-angle identities to find all solutions on the ...
Pre-Calc/Math - Use factoring, the quadratic formula, or identities to solve cos...
Trigonometry - Find all solutions of the equation in the interval [0,2pi] ...
URGENT - Trigonometry - Identities and Proofs - Okay, today, I find myself ...
trigonometry - Verify that following are identities: 1. cos 3t = 4 cos³ t-3...
Math-trigonometry - Several questions from my homework, any are appreciated. ...
trig - I need to find all solutions of the given equations for the indicated ...
trig - Find the exact solutions of the equation in the interval [0,2pi). sin(x/2...
trip - for sin2x+cosx=0, use double-angle or half-angle formula to simplify the ...
Pre-Calculus - cos^2(x) + sin(x) = 1 - Find all solutions in the interval [0, ...
For Further Reading
