Question

Please look at the image and help me with this homework problem if you can! thank you :)

Answer 1

Test for symmetry and then graph:

`r=2\cos \theta`

To test the symmetry with respect to the polar axis (the horizontal axis), we replace θ with -θ. If we get an equivalent equation, then the function is symmetric with respect to the polar axis.

`r=\cos (-\theta)`

Since cos θ = cos -θ:

r = cos θ

The equation is equivalent, thus the graph is symmetric with respect to the polar axis.

To test if the graph is symmetric with respect to the vertical axis, replace r with -r and θ with -θ. If the resulting equation is equivalent, the test is positive.

The function would take the form:

-r = 2cos -θ

-r = 2cos θ

r = -2cos θ

The equations are not equivalent, thus the graph is not symmetric with respect to the vertical axis.

To test if the graph is symmetric with respect to the pole (origin), substitute r by -r. This test fails, thus the only axis of symmetry found is the horizontal axis.