## anonymous 5 years ago sin 2x= 1/2

1. divanshu

x =15 deg

2. anonymous

because 1/2=sin30 = sin 2x therefore 2x=30 x=15

3. anonymous

Also, sine is positive in the second quadrant, so sine of 2x=(180-30) = 1/2 also. So x=75 degrees is a solution too.

4. anonymous

These are principle solutions. The general solution is $\theta = n.180^o+(-1)^n30^o$

5. anonymous

thats wrong i need it in the interval [0, 2 pi)

6. anonymous

You can convert from degrees to radians. It's equivalent, not wrong. $180^o = \pi^c \rightarrow 1^o=\frac{\pi^c}{180}\rightarrow 15^o=\frac{15\pi}{180}=\frac{\pi}{12}$

7. anonymous

8. anonymous

yes

9. anonymous

would 5 pi / 12 be equl to it to?

10. anonymous

$75^o=\frac{75\pi}{180}=\frac{5\pi}{12}$

11. anonymous

yes

12. anonymous

I need the multiple angle equation of x/2 = negative square root of 3/ 2

13. anonymous

Can you be clearer?

14. anonymous

cos x/2= - square root 3 /2

15. anonymous

Cosine in negative in the second and third quadrants. So, given cos(theta)=sqrt(3)/2 implies theta = 30 degrees, the angles needed here are: (i) 180-30 = 150 (ii) 180+30 = 210

16. anonymous

So (i) x = 300 (ii) x = 420 which you convert to radians, and then subtract integral multiples of 2pi until the angle lies in your principal domain [0,2pi) here.

17. anonymous

yeah i need it in the principal domain [0, 2 pi)

18. anonymous

please hurry up this test is due in 15 minutes and i am clueless

19. anonymous

hey gut that has been helping me

20. anonymous

wtf, i'm not your lackey. just put down 5pi/3

21. anonymous

lol, calm down loki ^_^