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СИСТЕМИ ТРИГОНОМЕТРИЧНИХ РІВНЯНЬ
або
ВИДЕО УРОК
1. Розв’яжіть систему рівнянь:
y =
π/4 ∙ (k – n), n, k ∈ Z;
б) x =
π/2 ∙ (k + n),
y =
π/2 ∙ (k – n), n, k ∈ Z;
в) x =
π/4 ∙ (k + n),
y =
π/2 ∙ (k – n), n, k ∈ Z;
г) x =
π/4 ∙ (k + n),
y =
π/4 ∙ (k – n), n, k ∈ Z.
y =
(–1)k ∙ π/6 + 2πk, n, k ∈ Z;
б) x =
±3π/4 + 2πn.
y =
(–1)k ∙ π/6 + πk, n, k ∈ Z;
в) x =
±3π/4 + πn.
y =
(–1)k ∙ π/6 + πk, n, k ∈ Z;
г) x =
±3π/4 + πn.
y =
(–1)k ∙ π/6 + 2πk, n, k ∈ Z.
y = 1/3
arctg 1/3 + πn/3,
n, k ∈ Z;
б) x = 1/3
arctg 1/3 + π/4 + πn/3 + πk.
y = 1/3
arctg 1/3 + πn/3,
n, k ∈ Z;
в) x =
1/3
arctg 1/3 + π/2 + πn/3 + πk.
y = 1/3
arctg 1/3 + πn/6,
n, k ∈ Z;
г) x =
1/3
arctg 1/3 + π/2 + πn/3 + πk.
y = 1/3
arctg 1/3 + πn/3,
n, k ∈ Z.
y =
5π/4 + πn, n, m ∈ Z;
б) x =
π/4 +
πm.
y =
5π/4 + 2πn, n, m ∈ Z;
в) x =
π/4 +
2πm.
y =
5π/4 + 2πn, n, m ∈ Z;
г) x =
π/4 +
2πm.
y =
5π/4 + πn, n, m ∈ Z.
x2 =
–π/8, y2 =
π/8;
б) x1 = π/4, y1 =
–π/8.
x2 =
–π/4, y2 =
π/8;
в) x1 = π/8, y1 =
–π/4.
x2 =
–π/8, y2 =
π/4;
г) x1 = π/4, y1 =
–π/4.
x2 =
–π/4, y2 =
π/4.
y1
= ±π/3 + 2πm.
x2
= ±π/3 + 2πk,
y2 = π/2 + 2πl, n, m, k, l ∈
Z;
б) x1
= π/2 + πn,
y1
= ±π/3 + πm.
x2
= ±π/3 + πk,
y2 = π/2 + πl, n, m, k, l ∈
Z;
в) x1 = π/2 + πn,
y1 =
±π/3 + 2πm.
x2 =
±π/3 + 2πk,
y2 = π/2 + πl, n, m, k, l ∈ Z;
г) x1 = π/2 + 2πn,
y1 =
±π/3 + πm.
x2 =
±π/3 + πk,
y2 = π/2 + 2πl, n, m, k, l ∈ Z.
y = –360° ∙ n;
б) x =
–60° + 360° ∙ n.
y = –360° ∙ n;
в) x =
–60° + 360° ∙ n.
y = 360° ∙ n;
г) x =
60° + 360° ∙ n.
y = 360° ∙ n.
y =
–π/8 –
πn/2, n ∈ Z;
б) x =
3π/8 + πn/2.
y =
–π/4 –
πn/2, n ∈ Z;
в) x =
3π/4 + πn/2.
y =
–π/4 –
πn/2, n ∈ Z;
г) x =
3π/8 + πn/2.
y =
–π/8 –
πn/2, n ∈ Z.
y =
1/6 – 2n, n ∈ Z;
б) x =
1/6 + 2n.
y =
1/6 – 2n, n ∈ Z;
в) x =
1/6 + 2n.
y =
1/6 – n, n ∈ Z;
г) x =
1/6 + n.
y =
1/6 – n, n ∈ Z.
y =
π/6 –
πn, n ∈ Z;
б) x =
π/6 +
2πn.
y =
π/6 –
2πn, n ∈ Z;
в) x =
π/6 +
πn.
y =
π/6 –
2πn, n ∈ Z;
г) x =
π/6 +
πn.
y =
π/6 –
πn, n ∈ Z.
y =
π/6 –
πn/2, n ∈ Z;
б) x =
π/2 +
πn/2.
y =
π/3 –
πn/2, n ∈ Z;
в) x =
π/2 +
πn/2.
y =
π/6 –
πn/2, n ∈ Z;
г) x =
π/4 +
πn/2.
y =
π/3 –
πn/2, n ∈ Z.
y =
π/2 +
2πk, k ∈ Z;
б) x =
2πn, n ∈ Z.
y =
π/2 +
2πk, k ∈ Z;
в) x =
πn, n ∈ Z.
y =
π/2 +
πk, k ∈ Z;
г) x =
2πn, n ∈ Z.
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