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Bledans
@Bledans
October 2021
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uekmyfhfp
1. tg x = sgrt3;
x= pi/3 + pi*k. Ответ 2)
2. sin 2x= sgrt2/2;
2x = (-1)^n*pi/4 + pi*n
x= (-1)^n*pi/8 + pi*n/2 Ответ 1)
3. cos(3pi/2 - x)= 1/2;
- sin x=1/2;
sinx = -1/2;
x=(-1)^k+1*pi/6 +pi*k, k∈Z.
4. tg(3pi/2 +x)= - sgrt3;
- ctg x= - sgrt 3;
ctg x= sgrt3;
x = pi/6 + pik, k∈Z.
5. 4 sin (x/4) cos(x/4)= -sgrt3;
2 sin(x/2)= - sgrt 3;
sin(x/2)= - sgrt3/2;
x/2 =(-1)k+1 * pi/3 + pi*k;
x= (-1)^k+1* 2pi/3 + 2pi*k; k∈Z.
6. cos^(3x)- sin^2(3x) = -1/2;
cos(6x)= -1/2;
6x= + - 2pi/3 + 2pi*k;
x= + - pi/9 + pi*k/3, k∈Z.
7. sin (pi/ 3 +x) - 1/2 =0;
sin(pi/3 +x)=1/2;
pi/3 +x=pi/6 +2pik; ⇒x= -pi/6 + 2pik; k∈Z.
или
pi/3 +x = 5pi/6 +2 pik; ⇒ x= pi/2 + 2pi*k,k∈Z
Ответ: х = - pi/6 + 2pik или x= pi/2 + 2pik, k∈Z.
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Answers & Comments
x= pi/3 + pi*k. Ответ 2)
2. sin 2x= sgrt2/2;
2x = (-1)^n*pi/4 + pi*n
x= (-1)^n*pi/8 + pi*n/2 Ответ 1)
3. cos(3pi/2 - x)= 1/2;
- sin x=1/2;
sinx = -1/2;
x=(-1)^k+1*pi/6 +pi*k, k∈Z.
4. tg(3pi/2 +x)= - sgrt3;
- ctg x= - sgrt 3;
ctg x= sgrt3;
x = pi/6 + pik, k∈Z.
5. 4 sin (x/4) cos(x/4)= -sgrt3;
2 sin(x/2)= - sgrt 3;
sin(x/2)= - sgrt3/2;
x/2 =(-1)k+1 * pi/3 + pi*k;
x= (-1)^k+1* 2pi/3 + 2pi*k; k∈Z.
6. cos^(3x)- sin^2(3x) = -1/2;
cos(6x)= -1/2;
6x= + - 2pi/3 + 2pi*k;
x= + - pi/9 + pi*k/3, k∈Z.
7. sin (pi/ 3 +x) - 1/2 =0;
sin(pi/3 +x)=1/2;
pi/3 +x=pi/6 +2pik; ⇒x= -pi/6 + 2pik; k∈Z.
или
pi/3 +x = 5pi/6 +2 pik; ⇒ x= pi/2 + 2pi*k,k∈Z
Ответ: х = - pi/6 + 2pik или x= pi/2 + 2pik, k∈Z.