Answer: y-axis.Explanation:The equation <span>r = 3 - 4 sin θ may be graphed using
cartesian coordinates (i.e. x and y) or polar coordinates.The logical way is to graph in polar coordinates. I did it using </span>a
graphing software and obtained the
attached graph.
Also, I attached the graph in cartesian coordinates.
Here you have a
table that you can build by your self and use the pairs to draw the graph (either cartesian or polar coordinates).
<span>
<span><span>
θ (rad)
r = 3 - 4 sin θ
</span>
<span>
0
3
</span>
<span>
π/8
2.61731657
</span>
<span>
π/4
2.29289322
</span>
<span>
3π/8
2.07612047
</span>
<span>
π/2
2
</span>
<span>
5π/8
2.07612047
</span>
<span>
3π/4
2.29289322
</span>
<span>
7π/8
2.61731657
</span>
<span>
π
3
</span>
<span>
9π/8
3.38268343
</span>
<span>
5π/4
3.70710678
</span>
<span>
11π/8
3.92387953
</span>
<span>
3π/2
4
</span>
<span>
13π/8
3.92387953
</span>
<span>
7π/4
3.70710678
</span>
<span>
15π/8
3.38268343
</span>
<span>
2π
3
</span>
</span></span>
In both of the attached graphs you can see that
the left side is equal to the right side, but the upper side is not equal to the bottom side.
Therefore, the graph is symmetric about the y-axis.
and 
to simplify our trig expression:
