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СИСТЕМИ ТРИГОНОМЕТРИЧНИХ РІВНЯНЬ
або
ВИДЕО УРОК
1. Розв’яжіть систему рівнянь:
y1 =
4π/3 + 2πn.
x2 =
4π/3 + πk,
y2 = –π/3 + 2πk, n, k ∈ Z;
б) x1 = 3π – 2πn,
y1 =
4π/3 + 2πn.
x2 =
4π/3 + 2πk,
y2 = –π/3 + 2πk, n, k ∈ Z;
в) x1 = 3π – 2πn,
y1 =
4π/3 + πn.
x2 =
4π/3 + 2πk,
y2 = –π/3 + πk, n, k ∈ Z;
г) x1 = 3π – πn,
y1 =
4π/3 + πn.
x2 =
4π/3 + πk,
y2 = –π/3 + πk, n, k ∈ Z.
y =
π/4 – 2πn, n ∈ Z;
б) x =
π/4 + πn,
y =
π/4 – 2πn, n ∈ Z;
в) x =
π/4 + 2πn,
y =
π/4 – πn, n ∈ Z;
г) x =
π/4 + πn,
y =
π/4 – πn, n ∈ Z.
y1
= arctg 1/3 + πk.
x2
= π/4 –
arctg 1/2 – 2πn,
y2 = arctg 1/2 + πn, n, k ∈
Z;
б) x1
= π/4 –
arctg 1/3 – 2πk,
y1
= arctg 1/3 + 2πk.
x2
= π/4 –
arctg 1/2 – 2πn,
y2 = arctg 1/2 + 2πn, n, k ∈
Z;
в) x1 = π/4 – arctg 1/3 – πk,
y1
= arctg 1/3 + πk.
x2
= π/4 –
arctg 1/2 – πn,
y2 = arctg 1/2 + πn, n, k ∈
Z;
г) x1 = π/4 – arctg 1/3 – πk,
y1
= arctg 1/3 + 2πk.
x2
= π/4 –
arctg 1/2 – πn,
y2 = arctg 1/2 + 2πn, n, k ∈
Z.
y =
–π/12 + πk/2, k ∈ Z;
б) x = 7π/12 + πk/2,
y =
π/12 + πk/2, k ∈ Z;
в) x =
–7π/12 + πk/2,
y =
–π/12 + πk/2, k ∈ Z;
г) x =
–7π/12 + πk/2,
y =
π/12 + πk/2, k ∈ Z.
y1 =
–π/3 + πn.
x2 =
π/3 + 2πk,
y2 = π/6 + πk, n, k ∈ Z;
б) x1 = –π/6 + 2πn,
y1 =
–π/3 + 2πn.
x2 =
π/3 + 2πk,
y2 = π/6 + πk, n, k ∈ Z;
в) x1 = –π/6 + πn,
y1 =
–π/3 + 2πn.
x2 =
π/3 + πk,
y2 = π/6 + 2πk, n, k ∈ Z;
г) x1 = –π/6 + πn,
y1 =
–π/3 + πn.
x2 =
π/3 + πk,
y2 = π/6 + πk, n, k ∈ Z.
y =
π/4 + πn/2 – πk, n, k ∈ Z;
б) x =
–π/4 + πn/2 + πk,
y =
π/4 + πn/2 – πk, n, k ∈ Z;
в) x =
–π/4 + πn/2 + πk,
y =
π/4 + πn/2 – 2πk, n, k ∈ Z;
г) x =
–π/4 + πn/2 + 2πk,
y =
π/4 + πn/2 – 2πk, n, k ∈ Z.
y1 =
π/6 + πk/2 – πn.
x2 =
π/6 + πk/2 + 2πn,
y2 = π/3 + πk/2 – πn, n, k ∈ Z;
б) x1 = π/3 + πk/2 + 2πn,
y1 =
π/6 + πk/2 – 2πn.
x2 =
π/6 + πk/2 + 2πn,
y2 = π/3 + πk/2 – 2πn, n, k ∈ Z;
в) x1 = π/3 + πk/2 + πn,
y1 =
π/6 + πk/2 – πn.
x2 =
π/6 + πk/2 + πn,
y2 = π/3 + πk/2 – πn, n, k ∈ Z;
г) x1 = π/3 + πk/2 + πn,
y1 =
π/6 + πk/2 – 2πn.
x2 =
π/6 + πk/2 + πn,
y2 = π/3 + πk/2 – 2πn, n, k ∈ Z.
y =
1/4 + 1/2 n + k, n, k ∈ Z;
б) x =
1/2 n –
2k –
1/4,
y =
1/4 + 1/2 n + k, n, k ∈ Z;
в) x =
1/2 n –
2k –
1/4,
y =
1/4 + 1/2 n + 2k, n, k ∈ Z;
г) x =
1/2 n –
k – 1/4,
y =
1/4 + 1/2 n + 2k, n, k ∈ Z.
y1 =
2π/3 + 2πk.
x2 =
πn,
y2 = –2π/3 + 2πk,
x3 = 2π/3 + πk,
y3 =
2πn.
x4 =
–2π/3 + πk,
y4 = 2πn, n, k ∈ Z;
б) x1 = 2πn,
y1 =
2π/3 + πk.
x2 =
2πn,
y2 = –2π/3 + πk,
x3 = 2π/3 + 2πk,
y3 =
πn.
x4 =
–2π/3 + 2πk,
y4 = πn, n, k ∈ Z;
в) x1 = 2πn,
y1 =
2π/3 + 2πk.
x2 =
2πn,
y2 = –2π/3 + 2πk,
x3 = 2π/3 + 2πk,
y3 =
2πn.
x4 =
–2π/3 + 2πk,
y4 = 2πn, n, k ∈ Z;
г) x1 = πn,
y1 =
2π/3 + πk.
x2 =
πn,
y2 = –2π/3 + πk,
x3 = 2π/3 + πk,
y3 =
πn.
x4 =
–2π/3 + πk,
y4 = πn, n, k ∈ Z.
y1 =
2πn.
x2 =
2πn,
y2 = –π/3 + 2πn, n ∈ Z;
б) x1 = π/3 + πn,
y1 =
2πn.
x2 =
πn,
y2 = –π/3 + 2πn, n ∈ Z;
в) x1 = π/3 + πn,
y1 =
πn.
x2 =
πn,
y2 = –π/3 + πn, n ∈ Z;
г) x1 = π/3 + 2πn,
y1 =
πn.
x2 =
2πn,
y2 = –π/3 + πn, n ∈ Z.
y1 =
2πn.
x2 =
2πn,
y2 = –π/3 + 2πn, n ∈ Z;
б) x1 = π/3 + πn,
y1 =
2πn.
x2 =
πn,
y2 = –π/3 + 2πn, n ∈ Z;
в) x1 = π/3 + πn,
y1 =
πn.
x2 =
πn,
y2 = –π/3 + πn, n ∈ Z;
г) x1 = π/3 + 2πn,
y1 =
πn.
x2 =
2πn,
y2 = –π/3 + πn, n ∈ Z.
y =
(–1)k ∙ π/6 – π/6 + πk/2, k ∈ Z;
б) x =
(–1)k ∙ π/6 + π/6 + πk/2.
y =
(–1)k ∙ π/6 – π/6 + πk/2, k ∈ Z;
в) x =
(–1)k ∙ π/6 + π/6 – πk/2.
y =
(–1)k ∙ π/6 – π/6 – πk/2, k ∈ Z;
г) x =
(–1)k ∙ π/6 + π/6 + πk/2.
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