1)sin(x-pi/4)=1

2)sin(x/4)*cos(x/4)=-1/4

3)(cos2x+cospi/4)*(cos2x+4)=0 {0;Pi}

4)sqrt3cosX+sin2x=0

5)sinx+sin5x=0

6)sin^2x-0.5sin2x=0

7)sin2x+sin6x=cos2x

8)3sin^2x+3cosx*sinx+2cos^2x=1

1

Ответы и объяснения

2013-05-14T16:51:01+04:00

1) sin(x-пи/4) = 1

x ∈ {2*пи*k+3*пи/4}, k ∈ Z

2)sin(x/4)*cos(x/4) = - 1/4

x ∈ {4*пи*k-5*пи/3, 4*пи*k-пи/3}, k ∈ Z

3)(cos(2*x)+cos(пи/4))*cos(2*x+4) = 0

x ∈ {пи*k-3*пи/8, пи*k+3*пи/8, (4*пи*k+asin(2*cos(4)*sin(4)*корень(sin(4)^4-2*cos(4)^2*sin(4)^2+cos(4)^4)/(sin(4)^2*корень(sin(4)^4+2*cos(4)^2*sin(4)^2+cos(4)^4)-cos(4)^2*корень(sin(4)^4+2*cos(4)^2*sin(4)^2+cos(4)^4))))/4, (4*пи*k+asin(2*cos(4)*sin(4)*корень(sin(4)^4-2*cos(4)^2*sin(4)^2+cos(4)^4)/(sin(4)^2*корень(sin(4)^4+2*cos(4)^2*sin(4)^2+cos(4)^4)-cos(4)^2*корень(sin(4)^4+2*cos(4)^2*sin(4)^2+cos(4)^4)))+2*пи)/4}, k ∈ Z

4)корень(3)*cos(x)+sin(2*x) = 0

x ∈ {2*пи*k-2*пи/3, 2*пи*k-пи/2, 2*пи*k-пи/3, 2*пи*k+пи/2}, k ∈ Z

5)sin(x)+sin(5*x) = 0

x ∈ {2*пи*k, 2*пи*k-3*пи/4, 2*пи*k-2*пи/3, 2*пи*k-пи/3, 2*пи*k-пи/4, 2*пи*k+пи/4, 2*пи*k+пи/3, 2*пи*k+2*пи/3, 2*пи*k+3*пи/4, 2*пи*k+пи}, k ∈ Z

6)sin(-0.5°)^(2*x)*sin(2*x) = 0

x=10; x∈{1.5707963267949*k}, k ∈ Z

7)sin(2*x)+sin(6*x) = cos(2°)

x 0.136384824009198, x 0.496532030300311, x=1.07426429649459, x=9.92130999106969

8)3*sin(x)^2+3*cos(x)*sin(x)+2*cos(x)^2 = 1

x ∈ {пи*k-пи/4, (2*пи*k-asin(4/5))/2}, k ∈ Z