Question 488238
.
sin 2x + cos 60 = 0, 0 < x < 360.
i have been able to find out that sin inverse of -1/2 is -30, but how do i find answers in the 3rd and fourth quadrant 
for 2x?? then i can find x. my answers are coming wrong, and i can apply no suitable rule. please help, and show 
working if possible.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~



In the post by @Theo, you will not find the answers for x,
so, the reader is in the dark about how to complete the solution.


I came to make the job from the beginning to the end.



<pre>
The starting equation is in degrees

    sin(2x) + cos(60°) = 0.


As you know, cos(60°) = -1/2,  so, you equation becomes

    sin(2x) + 1/2 = 0,  or  sin(2x) = -1/2.


You should know the table angles.  If sin(2x) = -1/2, it means
that angle 2x is in 3rd or 4th quadrant

    2x = 210°  or  2x = 330°.


It implies that  x = 210°/2 = 105°  or  x = 330°/3 = 165°.


<U>ANSWER</U>.  The given equation has two solutions,  x = 105°  and/or  x = 165°.
</pre>

Solved from the beginning to the end, with complete explanations
(and without pronouncing unnecessary and excessive words).