Решите уравнение cosx/2=-√ 2/2

Question

Решите уравнение cosx/2=-√ 2/2

Answer 1

Cos(x/2) = - √2/2
x/2 = (+ -)arccos(-√2/2) + 2πk, k∈Z
x/2 = (+ -)(π - arccos(√2/2)) + 2πk, k∈Z
x/2 = (+ -)(π - (π/4)) + 2πk, k∈Z
x/2 = (+ -)(3π/4) + 2πk, k∈Z
x = (+ -)(3π/2) + 4πk, k∈Z