anonymous
  • anonymous
sin 2x= 1/2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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divanshu
  • divanshu
x =15 deg
anonymous
  • anonymous
because 1/2=sin30 = sin 2x therefore 2x=30 x=15
anonymous
  • 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.

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anonymous
  • anonymous
These are principle solutions. The general solution is \[\theta = n.180^o+(-1)^n30^o\]
anonymous
  • anonymous
thats wrong i need it in the interval [0, 2 pi)
anonymous
  • anonymous
You can convert from degrees to radians. It's equivalent, not wrong. \[180^o = \pi^c \rightarrow 1^o=\frac{\pi^c}{180}\rightarrow 15^o=\frac{15\pi}{180}=\frac{\pi}{12}\]
anonymous
  • anonymous
do you know the answer
anonymous
  • anonymous
yes
anonymous
  • anonymous
would 5 pi / 12 be equl to it to?
anonymous
  • anonymous
\[75^o=\frac{75\pi}{180}=\frac{5\pi}{12}\]
anonymous
  • anonymous
yes
anonymous
  • anonymous
I need the multiple angle equation of x/2 = negative square root of 3/ 2
anonymous
  • anonymous
Can you be clearer?
anonymous
  • anonymous
cos x/2= - square root 3 /2
anonymous
  • 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
anonymous
  • 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.
anonymous
  • anonymous
yeah i need it in the principal domain [0, 2 pi)
anonymous
  • anonymous
please hurry up this test is due in 15 minutes and i am clueless
anonymous
  • anonymous
hey gut that has been helping me
anonymous
  • anonymous
wtf, i'm not your lackey. just put down 5pi/3
anonymous
  • anonymous
lol, calm down loki ^_^

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