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

Question

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

r = 3 – 4 sin θ

in progress 0

1. y-axis… just look at the graph on desmos.com

2. Explanation:

The equation r = 3 – 4 sin u03b8 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).

n n u03b8 (rad) n r = 3 – 4 sin u03b8n n n

0n 3n n n
u03c0/8n 2.61731657n
n
n u03c0/4 n 2.29289322n n n
3u03c0/8n 2.07612047n
n n u03c0/2n 2n
n n 5u03c0/8 n 2.07612047n n n
3u03c0/4n 2.29289322n
n n
7u03c0/8n 2.61731657n
n n
u03c0n 3n
n n
9u03c0/8n 3.38268343n
n n
5u03c0/4n 3.70710678n
n n
11u03c0/8n 3.92387953n
n n
3u03c0/2n 4n
n n
13u03c0/8n 3.92387953n
n n
7u03c0/4n 3.70710678n
n n
15u03c0/8n 3.38268343n
n n
2u03c0n 3n
n

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.