How do I solve sin( theta/ 2 ) − 1 = 0? Find all solutions of the equation & the solutions in the interval [0, 2π).

1 Answer
Mar 20, 2018

#theta = pi#

Explanation:

Given: #sin(theta/2) - 1 = 0# in the interval #[0, 2pi)#

Solve: #sin(theta/2) = 1#

Let #beta = theta/2; " " theta = 2 beta#

Solve: # sin beta = 1#

From a trigonometric (unit circle): #beta = pi/2 => sin (pi/2) = 1#

If #beta = pi/2; " " theta = 2 * beta = 2 * pi/2 = pi#

#theta = pi#