solve each equation on the interval [0,2pi)?

Question

1. sin x = 1/2
2. cos^2x= cosx
3. 2cosx + sqrt3=0
4. 4sin^2x=1
5. 2sin^2 x + sinx=1
6. cos^2 x + 2cosx=3
7. 2sin x cos x +sin x=0
8. 8cos^2 x - 2cos x=1
9. sin^2 x - cos^2 x=0

Answer 1

1♥ x1= 30°, x2= 180-30=150°;
2♠ cosx (cosx –1)=0, hence cos(x1) =0,
hence x1=90°, x2= 180+90° =210;
also cosx=1, hence x3=0;
3♥ cosx =-√3 /2; x1=30, x2= 180+30 =210;
4♠ sinx =±1/2; x1=30°, x2=30+180=210, x3= 360-30 =330, x4=330-180=150;
5♥ 2s^2 +s –1=0; s= (-1±√(1+4*2))/(2*2) =(-1±3)/4 =-1, 0.5;
sinx=-1, hence x1=270°; sinx=0.5, hence x2=30, x3=150°;
6♠ c^2 +2c –3=0, c=-1±√(1+3) = -1±2 =-3, 1;
cosx =-3 is bullshyt! Cosx=1; x=0;
7♥ sinx (2cosx +1) =0; sinx=0, hence x1=0, x2=180;
also cosx =-0.5, hence x3=60+180=240, x4=180-60=120;
8♠ 8c^2 –2c –1=0; c= (1±√(1+8*1))/8 =(1±3)/8 = -1/4, 1/2;
x1=180+acos(1/4), x1=180-acos(1/4),
9♥ -cos(2x)=0; 2*x1=90, x1=45; 2*x2=270, x2=135;
2*x3 = 270+180, x3=225; 2*x4=270+360, x4=315;

Answer 2

enable the thetas be x. 2cos^2 x + cos x = 0 cos x (2cos x + a million) = 0 Cos x = 2 or 2cos x + a million = 0 Cos x = 2 (N/A with the aid of fact that -a million

Answer 3

You've got to be kidding!!