Question

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

r = 4 - 3 sin θ

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

r = 2 cos 5θ

Answer 1

http://www.wolframalpha.com/input/?i=y%3D4-3sinx%2C+y%3D2cos5x

Answer 2

1. Origin only
2. y- axis only
@larryboxaplenty

Answer 3

1. no symmetry*

Answer 4

@larryboxaplenty are these right?

Answer 5

y1 = 4 - 3sin x y2 2cos 5x
To determine the symmetry, you have to create a variation table of the 2 equations, with x varies from -Pi to +Pi.

x | -Pi -Pi/2 0 Pi/2 Pi
-------------------------------------------------
y1 | 4 7 4 1 4
--------------------------------------------------
y2 | -2 0 2 0 -2

By a rough graph, you will see that y1 is symmetric about the origin O.
the graph y2 is symmetric about the y axis.

Answer 6

@thu1935 so 1. is origin only and 2. is y axis only?

Answer 7

yes.

Answer 8

I think if you know the basic shape of the graphs of sinx and cosx, you can easily answer the question. Notice that translations in the y-axis direction and dilations don't do anything to the symmetry of a graph, which is the case in the two functions you gave...