8. 1-Б; 2-Г; 3-А; 4-В.
9. 1-Д; 2-Б; 3-Г; 4-А.
Подробнее объяснение:
8. 1) 2cosx = 1
cosx = 1/2
x = ± arccos1/2 + 2πn, n є Z
x = ± π/3 + 2πn, n є Z. Б.
2) 2cosx/2 = 1
cosx/2 = 1/2
x/2 = ± arccos1/2 + 2πn, n є Z
x/2 = ± π/3 + 2πn, n є Z.
x = ± 2π/3 + 4πn, n є Z. Г.
3) cos2x = 1
2x = ± arccos1/2 + 2πn, n є Z
2x = ± π/3 + 2πn, n є Z.
x = ± π/6 + πn, n є Z. А.
4) cosx/2 = 1
x/2 = 2πn, n є Z.
x = 4πn, n є Z. В.
Відповідь: 1-Б; 2-Г; 3-А; 4-В.
9. 1) sin2x = 0. [0; 2π] sinx є [-1; 1]
2x = πn, n є Z
x = πn/2, n є Z n = 0, x = 0 +
n = 1, x = π/2. +
n = 2, x = π +
n = 3, x = 3π/2 +
n = 4, x = 2π. +
n = 5, x = 5π/2 -
П'ять коренів. Д.
2) sin2x = 1. [0; 2π]
2x = π/2 + 2πk, k є Z.
x = π/4 + πk, k є Z.
k = 0, x = π/4. +
k = 1, x = 5π/4. +
k = 2, x = 9π/4. -
Два корені. Б.
3) cos2x = 0. [0; 2π]
2x = π/2 + πm, m є Z.
x = π/4 + πm/2, m є Z.
m = 0, x = π/4. +
m = 1, x = 3π/4. +
m = 2, x = 5π/4. +
m = 3, x = 7π/4. +
m = 4, x = 9π/4. -
Чотири корені. Г.
4) tgx/2 = 1. [0; 2π]
x/2 = arctg1 + πt, t є Z.
x/2 = π/4 + πt, t є Z.
x = π/2 + 2πt, t є Z.
t = 0, x = π/2 . +
t = 1, x = 5π/2. -
Один корінь. А.
Відповідь: 1-Д; 2-Б; 3-Г; 4-А.
