Question

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

Answer 1

see picture, it is symmetrical about the Y axis

Answer 2

Answer:

Symmetry about y-axis

Step-by-step explanation:

We are given that

$r=4-3sin\theta$

When the graph is symmetric about x- axis then the point (x,y) change in to (x,-y) and the function remain same.

The point$(r,\theta,)$ is replaced by $( r,-\theta)$

Substitute the value then we get

$r=4-3 sin(-\theta)$

$r=4+3sin\theta$  ($sin(-\theta)=-sin\theta)$

The value of function changes .Hence , the function is not symmetric about x- axis.

When the function is symmetric about y-axis then the point $(r,\theta)$ change into point $(r,\pi-\theta)$ and function remain same

Substitute the value

$r=4-3sin(\pi-\theta)$

$r=4-3 sin\theta$  ($sin(\pi-\theta)=sin\theta$)

The value of function does not change when point change ,Hence, the function is symmetric about y- axis.

When the graph is symmetric about origin then the point  $(\theta,r)$ change into point$(r,\pi+\theta)$ and the value of function remain same.

Substitute the value then we get

$r=4-3sin(\pi+\theta)$

$r=4+3sin\theta$

$r=4+3sin\theta$

Hence, the graph has  symmetry about y-axis .