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

Symmetric about the y-axis only

Step-by-step explanation:

Graph the function using a calculator

alternatively,

Sketch the graph via the following steps

-sketch cosθ

- reflect about the x-axis to get (- cosθ)

- multiply vertex values by 4 to get -4cosθ

- shift the graph in the positive y direction by 4 units to get 4 - 4cosθ

you will end up with the attached graph:

By observation, we can see that the graph is

1) NOT symmetric about the x-axis

2) Symmetric about the y-axis

3) Not symmetric bout the origin

to run a symmetry test on a polar, we can simply do a few ( r , θ ) replacements, if the equation resulting from the replacements, resembles the original, then it has that symmetry type, now, let's recall the symmetry trigonometry identity, cos(-θ) = cos(θ).

a

step-by-step explanation:

this is the formula: v = the value of investment at the end of the time period

p = the principal amount (the initial amount invested)

r = the annual interest rate

n = the annual frequency of compounding (how many times a year interest is added)

t = the number of years the money is invested

^ means raise to the power of