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What are the solutions to the equation on [0,2π) ?

csc(3x)=−2√3/3

 Apr 1, 2020
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csc (3x)  = -2√3/3  =  -2/√3

 

This  is  the  same as   sin (3x)   = -√3/2

 

Note  that   sin (x) =  -√3/2     at   (4/3)pi, (5/3)pi, (10/3)pi, (11/3)pi, (16/3)pi, (17/3)pi

 

Dividing each of these  by 3  we  get that

 

x = (4/9)pi, (5/9)pi, (10/9)pi, (11/9)pi, (16/9)pi, (17/9) pi

 

 

 

cool cool cool

 Apr 1, 2020

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