Найдите наименьшее решение уравнения cosx=1/2 [750; 1050]

750=750*pi / 180 = 25pi/6;

1050 = 1050*pi/180 = 35pi/6.

cos x = 1/2;

x = + - pi/3 + 2 pi*k; k-Z.

1) 25 pi/6 ≤ pi/3 + 2pik ≤ 35 pi/6;

25/6 ≤ 1/3 + 2k ≤35/6;

25/6 - 1/3 ≤ 2k ≤35/6 - 1/3;

23/6 ≤2k ≤33/6;

23/12 ≤ k ≤ 33/12.

k = 2.⇒x = pi/3 + 2pi*2 = pi/3 + 4 pi = 13pi/3 = 13*180 / 3 = = 780.

2)

25 pi/6 ≤ - pi/3 + 2pik ≤ 35 pi/6;

25/6 ≤ - 1/3 + 2k ≤35/6;

25/6 + 1/3 ≤ 2k ≤35/6 + 1/3;

27/6 ≤2k ≤37/6;

27/12 ≤ k ≤ 37/12.

k = 3; ⇒x = - pi/3 + 2*3pi = - pi/3 + 18 pi/3 = 17 pi/3=

= 17*180 / 3 = 17*60 = 1020.