Question

Find the area of the region enclosed by one loop of the curve. r=7cos(3θ)

Answer 1

The area of the region enclosed by the curve r = 7cos(3θ) is 49 times the square of the cosine of 3θ.

Step-by-step explanation:

The area of the region enclosed by one loop of the curve r = 7cos(3θ) can be found using the formula A = r².

Substituting the given value of r = 7cos(3θ), we have A = (7cos(3θ))².

Simplifying, A = 49cos²(3θ).

The area of the region enclosed by one loop of the curve is 49 times the square of the cosine of 3θ.

Answer 2

The area of the region enclosed by one loop of the curve can be found using the formula A = πr².

Step-by-step explanation:

The area of the region enclosed by one loop of the curve can be found using the formula A = πr². In this case, we are given r = 7cos(3θ). To find the area, substitute this value of r into the formula:

A = π(7cos(3θ))² = 49πcos²(3θ) m².

This is the equation for the area of the region enclosed by one loop of the curve.