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Natali [406]
3 years ago
14

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

Mathematics
2 answers:
8_murik_8 [283]3 years ago
7 0

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 .

Alisiya [41]3 years ago
3 0
See picture, it is symmetrical about the Y axis

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