How to find solutions to the following equations in the interval 0 ≤ x < 360?

Question

Find solutions to the following equations in the interval 0 ≤ x < 360◦. Round
answers to the nearest 10th degree.
3 sin x − 2 = 0

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Answer 1 · 2018-06-02T04:34:10

#x~~40^circ or x~~140^circ#

Here,

#3sinx-2=0 ,where, x in[0^circ,360^circ)#

#=>3sinx=2#

#=>sinx=2/3 > 0=>I^(st)Quadrant or II^(nd)Quadrant #

#(i) I^(st)Quadrant :#

#sinx=2/3=>x=sin^-1(2/3)#

#=>x~~(41.81)^circ=>x~~40^circ#

#(ii)II^(nd)Quadrant :#

#sinx=2/3=>x=180^circ-sin^-1(2/3)#

#=>x~~180^circ-(41.81)^circ#

#=>x~~(138.19)^circ#

#=>x~~140^circ#