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ФОРМУЛЫ КОРНЕЙ ТРИГОНОМЕТРИЧЕСКИХ УРАВНЕНИЙ. sin x = a. a) x = ± arcsin a + П k, k Z b) x = (–1) k arcsin a + П k, k Z c) x = ± arcsin a + 2 П k, k Z d) x = (–1) k arcsin a + 2 П k, k Z. sin x = a. a) x = ± arcsin a + П k, k Z - PowerPoint PPT Presentation
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3
П
sin x = a
• a) x = ± arcsin a + Пk, k Z
b) x = (–1)k arcsin a + Пk, k Z
c) x = ± arcsin a + 2Пk, k Z
d) x = (–1)k arcsin a + 2Пk, k Z
sin x = a
• a) x = ± arcsin a + Пk, k Z
b) x = (–1)k arcsin a + Пk, k Z
c) x = ± arcsin a + 2Пk, k Z
d) x = (–1)k arcsin a + 2Пk, k Z
cos x = a
• a) x = ± arccos a + Пk, k Z
b) x = (–1)k arccos a + Пk, k Z
c) x = ± arccos a + 2Пk, k Z
d) x = (–1)k arccos a + 2Пk, k Z
cos x = a
• a) x = ± arccos a + Пk, k Z
b) x = (–1)k arccos a + Пk, k Z
c) x = ± arccos a + 2Пk, k Z
d) x = (–1)k arccos a + 2Пk, k Z
cos x =
a) x = (–1)k + Пk, k Z
b) x = ± + Пk, k Z
c) x = ± + 2Пk, k Z
d) x = ± + 2Пk, k Z
2
1
3
П
6
П
3
П
6
П
cos x =
a) x = (–1)k + Пk, k Z
b) x = ± + Пk, k Z
c) x = ± + 2Пk, k Z
d) x = ± + 2Пk, k Z
2
1
3
П
6
П
3
П
6
П
sin x = –
a) x = (–1)k+1 + Пk, k Z
b) x = ± + Пk, k Z
c) x = (–1)k+1 + 2Пk, k Z
d) x = (–1)k+1 + Пk, k Z
2
1
3
П3
П
6
П
3
П
6
П
sin x = –
a) x = (–1)k+1 + Пk, k Z
b) x = ± + Пk, k Z
c) x = (–1)k+1 + 2Пk, k Z
d) x = (–1)k+1 + Пk, k Z
2
1
3
П3
П
6
П
3
П
6
П
sin x – 1 = 0
a) x = (–1)k + Пk, k Z
b) x = П + Пk, k Z
c) x = (–1)k+1 + Пk, k Z
d) x = + Пk, k Z
3
П
2
П
2
П
2
П
2
П
2
П
sin x – 1 = 0
a) x = (–1)k + Пk, k Z
b) x = П + Пk, k Z
c) x = (–1)k+1 + Пk, k Z
d) x = + 2Пk, k Z
3
П
2
П
2
П
2
П
2
П
2
П
соs x = 0
a) x = (–1)k + 2Пk, k Z
b) x = П + Пk, k Z
c) x = (–1)k + Пk, k Z
d) x = + Пk, k Z
3
П
2
П
2
П
2
П
2
П
2
П
соs x = 0
a) x = (–1)k + 2Пk, k Z
b) x = П + Пk, k Z
c) x = (–1)k + Пk, k Z
d) x = + Пk, k Z
3
П
2
П
2
П
2
П
2
П
2
П
tg x = 1
a) x = (–1)k + Пk, k Z
b) x = + Пk, k Z
c) x = + Пk, k Z
d) x = + 2Пk, k Z
3
П
4
П
4
П
4
П
4
П
4
3П
tg x = 1
a) x = (–1)k + Пk, k Z
b) x = + Пk, k Z
c) x = + Пk, k Z
d) x = + 2Пk, k Z
3
П
4
П
4
П
4
П
4
П
4
3П
tg x = – 3
a) x = – + Пk, k Z
b) x = arctg 3 + Пk, k Z
c) x = – arctg 3 + Пk, k Z
d) x = – arctg 3 + 2Пk, k Z
3
П
3
П
tg x = – 3
a) x = – + Пk, k Z
b) x = arctg 3 + Пk, k Z
c) x = – arctg 3 + Пk, k Z
d) x = – arctg 3 + 2Пk, k Z
3
П
3
П
ctg x = –
a) x = – + Пk, k Z
b) x = – + Пk, k Z
c) x = + Пk, k Z
d) x = + 2Пk, k Z
3
П
3
П
3
3
6
П
3
2П
6
5П
ctg x = –
a) x = – + Пk, k Z
b) x = – + Пk, k Z
c) x = + Пk, k Z
d) x = + 2Пk, k Z
3
П
3
П
33
6
П
3
2П
6
5П
3
П3
ДОМАШНЯЯ РАБОТА
1. 2sinx + 1 = 0, xЄ[0; 2π].
2. cos(2π – x) + sin(π/2 + x) = √2.
3. (sinx + cosx)2 = 1 + sinxcosx, xЄ[0; 2π].
4. sin(π/2 – x) = sin(– π/4).
5. 4cos2x – 1 = 0.
6. sin2x – 6 sinx = 0.
7. tgx + √3 = 0, xЄ[–2π; 0].
8. (sinx – 1)(tgx + 1) = 0.
9. 2 sin2x – sinx – 1 = 0.
10. 2 sinx + 3 cosx = 0.
11. cos2x – 3sinxcosx + 1 = 0
1. 2cosx – 1 = 0, xЄ[0; 2π].
2. 2cos(π/4 – 3x) = √2.
3. sin3xcosx – sinxcos3x = √3/2.
4. sin(π/2 – x) = sin(– π/4).
5. 2cos2x + sinx + 1 = 0.
6. 4sin2x – sin2x = 3.
7. 2tg2x – 9tgx – 5 = 0.
8. (sinx + 1)(tgx + √3) = 0.
9. cos5x – cos3x = 0.
