SOLUTION: solve equation sin x=0.5 where 0 < x < 360°

That involves a special angle.

You need to learn these three special right triangles, 
their sides, and their angles



Make the 0.5 into a fraction

sin x = 0.5 = 1/2 = opposite/hypotenuse

The fraction 1/2 has 1 for the numerator and 2 for the denominator.
Which one of those right triangles has 1 for the opposite side and 2
for the hypotenuse? It's this one:



The sine is positive in QI and QII

So we put that triangle into QI and QII, and we indicate the 
counter-clockwise rotation from the right side of the x-axis 
with a red arc:

Putting it in QI, we have this:



The red arc tells us that the counter-clockwise rotation from
the right side of the x-axis is through 30°, so the QI answer is

x = 30°

Now let's put that triangle in QII, notice that since the
adjacent side goes left of the origin, we must change the sign
of  to 



Now the red arc that measures the counter-clockwise rotation 
from the right side of the x-axis.  But it is not 30°, for 30°
is the reference angle.  The angle of the red arc is 180°-30°,
or 150°.

So the QII answer is

x = 150°.

Edwin