Question

An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)
sin(θ/2) − 1 = 0
(a) Find all solutions of the equation.
(b) Find the solutions in the interval [0, 2π).

Answer 1

Answer:

(a) θ = π + 4πn

(b) θ = π

Step-by-step explanation:

(a) sin(θ/2) − 1 = 0

sin(θ/2) = 1

θ/2 = π/2 + 2πn

θ = π + 4πn

(b) Try different values of n.

n = -1, θ = -3π

n = 0, θ = π

n = 1, θ = 5π

If 0 < θ < 2π, then θ = π.