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trig q

express the following equations for value of theta in the interval 0< theta < 2pie, give your answer in terms of pie

cosec1/2theta = 2 square root of 3 all over 3
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Malik
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LondonBoy
express the following equations for value of theta in the interval 0< theta < 2pie, give your answer in terms of pie

cosec1/2theta = 2 square root of 3 all over 3


cosec1/2x=(2&#8730;3)/3
sin1/2x=3/(2&#8730;3)
1/2x=60°=&#960;/3
x=120°=2&#960;/3
sin⁡x2=32\sin \frac{x}{2} = \frac{\sqrt{3}}{2}
x2=sin⁡−1(32)=2nπ+(π2±π6) \frac{x}{2} = \sin^{-1}( \frac{\sqrt{3}}{2}) = 2n\pi + (\frac{\pi}{2} \pm \frac{\pi}{6})
x=4nπ+(π±π3)x = 4n \pi + (\pi \pm \frac{\pi}{3})
n=0 is the only one which gives the required range of x. Therefore
x=π±π3x = \pi \pm \frac{\pi}{3}

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