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Chapter 9: Q. 13 (page 747)

Which kind(s) of symmetry does the roser=cos5胃have? How many petals does this curve have?

Which kind(s) of symmetry does the roser=sin8胃 have? How many petals does this curve have?

Short Answer

Expert verified

The rose r=cos5胃is symmetrical about x-axis and it has five petals.

The rose r=sin8胃is not symmetrical about the x-axis and y-axis. It has 16petals..

Step by step solution

01

Step 1. Given information

The equation of roses:

r=cos5胃r=sin8胃

02

Step 2. Find the symmetry and number of petals of r=cos5θ.

r(胃)=cos5胃r(-胃)=cos(-5胃)r(-胃)=cos5胃r(-胃)=r(胃)

So this is symmetrical about the x-axis.

r(蟺-胃)=cos5(蟺-胃)r(蟺-胃)=cos5(蟺-胃)r(蟺-胃)=cos(5蟺-5胃)r(蟺-胃)=cos(4蟺+蟺-5胃)r(蟺-胃)=cos(蟺-5胃)r(蟺-胃)=-cos(5胃)r(蟺-胃)=-r(胃)

This is not symmetrical about y-axis.

The graph of the function is

It has 5 petals.

03

Step 3. Find the symmetry and number of petals of r=sin8θ.

r(胃)=sin8胃r(-胃)=sin(-8胃)r(-胃)=-sin8胃r(-胃)=-r(胃)

So the graph is not symmetrical about the x-axis.

localid="1652355123216" r(蟺-胃)=sin8(蟺-胃)r(蟺-胃)=sin8(蟺-胃)r(蟺-胃)=-sin8胃r(蟺-胃)=-r胃

So the graph is not symmetrical about the y-axis.

So the graph is not symmetrical about the origin.

It has 16 petals.

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