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.

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sin(2x) + (1/2) = 0
sin(2x) = -1/2
2x = arcsin(-1/2) = 210 or 330
x = 105 or 165 degrees
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Note: If you know sin(theta) = 1/2
then sin(180-theta) = 1/2
and sin(180+theta) = -1/2
and sin(360-theta) = -1/2
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You can find those relationships
on the unit circle.

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Cheers,
Stan H.