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# Find ALL the solutions of the folloing equation that are in the interval [0, 2pi). 2cosx+1=0?

Hi please note that it says find ALL the solutions and note the brackets are different around the [0, 2pi). so far i have gotten that cosx=-1/2 . on the unit circle this is 2pi/3 and 4pi/3. i know you are supposed to add something to the end of this to make it be all the solutions but i forgot what it is and cant find it in my book. please check my work and give answer! thanks SO much <3

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- Anonymous1 decade agoFavorite Answer
There's nothing to add, you have the right answer.

- 4 years ago
3csc^2 x - 4 = 0 3csc^2 x = 4 csc^2 x = 4/3 sin^2 x = 3/4 sin x = ±?3/2 arcsin(?3/2) = 60°. So the reference attitude is 60°. In each and each quadrant, the corresponding angles are x = 60°, one hundred twenty°, 240°, 3 hundred° x = ?/3, 2?/3, 4?/3, 5?/3

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