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anonymous

  • 5 years ago

sin 2x= 1/2

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  1. divanshu
    • 5 years ago
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    x =15 deg

  2. anonymous
    • 5 years ago
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    because 1/2=sin30 = sin 2x therefore 2x=30 x=15

  3. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    These are principle solutions. The general solution is \[\theta = n.180^o+(-1)^n30^o\]

  5. anonymous
    • 5 years ago
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    thats wrong i need it in the interval [0, 2 pi)

  6. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    do you know the answer

  8. anonymous
    • 5 years ago
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    yes

  9. anonymous
    • 5 years ago
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    would 5 pi / 12 be equl to it to?

  10. anonymous
    • 5 years ago
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    \[75^o=\frac{75\pi}{180}=\frac{5\pi}{12}\]

  11. anonymous
    • 5 years ago
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    yes

  12. anonymous
    • 5 years ago
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    I need the multiple angle equation of x/2 = negative square root of 3/ 2

  13. anonymous
    • 5 years ago
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    Can you be clearer?

  14. anonymous
    • 5 years ago
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    cos x/2= - square root 3 /2

  15. anonymous
    • 5 years ago
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    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
    • 5 years ago
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    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
    • 5 years ago
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    yeah i need it in the principal domain [0, 2 pi)

  18. anonymous
    • 5 years ago
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    please hurry up this test is due in 15 minutes and i am clueless

  19. anonymous
    • 5 years ago
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    hey gut that has been helping me

  20. anonymous
    • 5 years ago
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    wtf, i'm not your lackey. just put down 5pi/3

  21. anonymous
    • 5 years ago
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    lol, calm down loki ^_^

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