precalc math problem 11

Question

Solve the equation for solutions in the interval ​[0,2π​).

Use algebraic methods and give exact values. Support your solutions graphically.

sin (x/2) = 1−sin(x/2)

Answer 1

2sin(x/2) = 1; sin(x/2) = 1/2; x/2 = π/6 or x/2 = 5π/6. So, x = π/3 or x = 5π/3.

Answer 2

sin(x/2) = 1-sin(x/2)

2sin(x/2) = 1

sin(x/2) = 1/2

x/2 = sin^-1(1/2) = pi/6 or 5pi/6

x = 2(pi/6) or 2(5pi/6)

x= pi/3 or 5pi/3