Question

Graph the curve and find the area that it encloses.

r = 2 + sin 4θ

Answer 1

Step 1:

The curve equation is .

Construct a table for different values of .

	2	2.866	2	1.134	2	2.866	2	1.134	2

Graph :

(1) Graph the polar co-ordinates.

(2) Plot the points.

(3) Connect the points with a smooth curve.

Graph of the curve is is :

Step 2 :

Area of the region enclosed by the curve is .

The boundaries of the curve are .

Area of the region enclosed by the curve :

Area of the region enclosed by the curve is square units.

Solution:

Graph of the curve is is 

Area of the region enclosed by the curve is square units.