1) sin x/2 = √3/2
x/2 = π/3 + πn, n∈Z
x = (2π)/3 + 2πn, n∈Z
2) cos 5x = 1/2
4x = +- π/3 + 2πn, n∈Z
x = +- π/12 + (πn)/2, n∈Z
3) tg (3x)/4 = 1
(3x)/4 = π/4 + πn, n∈Z
3x = π + 4πn, n∈Z
x = π/3 + (4πn)/3, n∈Z
4) ctg 4x = 0
4x = π/2 + πn, n∈Z
x = π/8 + (πn)/4, n∈Z
5) sin x = √2/2
x = π/4 + πn, n∈Z
6) cos x = 1/2
x = +- π/3 + 2πn, n∈Z
7) tg x = 1
x = π/4 + πn, n∈Z
8) ctg x = √3
x = π/6 + πn, n∈Z
9) tg x/2 = 3/2
x/2 = arctg 3/2 + πn, n∈Z
x = arctg 3 + 2πn, n∈Z
10) sin ((3x)/2 + π/3) + 1 = 0
sin ((3x)/2 + π/3) = -1
((3x)/2 + π/3) = - π/2 + 2πn, n∈Z
(3x)/2 = - π/2 - π/3 +2πn, n∈Z
(3x)/2 = - (5π)/6 + 2πn, n∈Z
x = - (5π)/9 + (4πn)/3, n∈Z
11) 2cos(2x-π/4)=1
cos(2x-π/4)=1/2
2x-π/4=+-π/3+2πn, n∈Z
2x=+-π/12+2πn, n∈Z
x=+-+-π/24+πn, n∈Z