# Trig Homework

Finding the Area of a Sector of a Circle

From Geometry it is known that the area of a sector of a circle is proportional to the

measure of the central angle. Consider the circle to the right to explore this.

1. Let the central angle be the entire circle or 2 radians. What is the area of this sector, which represents the area of the whole circle, or ___________?

2. Using proportions yields: 2 area of a sector

r= and solving the equation

for the area of a sector gives the equation, area of a sector =

:

Area of a Sector Theorem: The area A of the sector of a circle of radius r formed by a central

angle of θ radians is: A = area of a sector =

1. Find the area of the sector of a circle of radius 5 feet formed by an angle of 40°. Round the answer to two decimal places, if necessary.

2. Find the area of the sector of a circle of radius 3 𝑐𝑚 formed by an angle of 𝜃 = 2. Round your answer to two decimal places, if necessary.

3. Find the length of arc 𝑠 cut off by 𝜃, if 𝜃 = 𝜋