Circle Formulas

Question 1

Arc Length of a Circle

Answer 1

s=𝛳r (radians)

s=𝛳(π/180)r (degrees)

Question 2

Area of a Sector

Answer 2

A=(𝛳/360)πr^2 (if 𝛳 in degrees)

A=(𝛳/2)r^2 (if 𝛳 in radians)

Question 3

Linear speed of a point traveling along the circumference

Answer 3

(distance traveled)/time
v=s/t (s=arc length)
Miles per hour, feet per second, etc.

Question 4

Angular speed of a point traveling along the circumference

Answer 4

(angles swept out)/time
ω=𝛳/t
Independent of size of circle
radians per second, revolutions per minute

Question 5

How would you convert radians to degrees?

Answer 5

180/pi

Question 6

How would you change degrees to radians?

Answer 6

Pi/180