Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 3 - 4 sin θ

y-axis.

Explanation:

The equation 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 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).

θ (rad)    r = 3 - 4 sin θ

0               3
π/8            2.61731657
π/4            2.29289322
3π/8          2.07612047
π/2            2
5π/8          2.07612047
3π/4          2.29289322
7π/8          2.61731657
π               3
9π/8          3.38268343
5π/4          3.70710678
11π/8        3.92387953
3π/2          4
13π/8        3.92387953
7π/4          3.70710678
15π/8        3.38268343
2π             3

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.