Question 1194997
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Determine all the values where  -3*sinx = √3*cosx  for 0 <= x < 360 degrees.
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I specially re-wrote your formulation in order for

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;you learn on how to do it in a right way.



<pre>
Your original equation is

    -3*sin(x) = {{{sqrt(3)*cos(x)}}}.


Divide both sides by -3*cos(x).  You will get an EQUIVALENT equation

    tan(x) = {{{-sqrt(3)/3}}}.


In the given interval  0 <= x < 360  it has presicely two solutions

    x = 150 degrees  and  x = 330 degrees.    <U>ANSWER</U>
</pre>

Solved.


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A person who loves accurate mathematical solutions, &nbsp;may ask me why I divided the original
equation by &nbsp;cos(x) &nbsp;without taking care that &nbsp;cos(x) &nbsp;can be equal to &nbsp;0 &nbsp;(zero).



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It is right question.



The &nbsp;&nbsp;<U>answer</U> &nbsp;&nbsp;is&nbsp;: &nbsp;&nbsp;it is because if &nbsp;cos(x) = 0, &nbsp;then due to the given equation, &nbsp;sin(x) = 0;  

but &nbsp;sin(x) &nbsp;and &nbsp;cos(x) &nbsp;may not be equal to zero simultaneously.


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;So, &nbsp;the case &nbsp;cos(x) = 0 &nbsp;is &nbsp;EXCLUDED &nbsp;by the given equation &nbsp;(&nbsp;!&nbsp;)