11/3/22 - Radians

Question 1

What is the circumference of the unit circle?

Answer 1

2π units

Question 2

What are radians?

Answer 2

A way of measuring angles on the unit circle using the circle’s circumference.

Question 3

How do you convert degrees to radians?

Answer 3

Multiply by π/180

Question 4

How do you convert radians to degrees?

Answer 4

Multiply by 180/π

Question 5

If 360 degrees = 2π radians, how many radians are in 180 degrees?

Answer 5

π radians

Question 6

What is 90 degrees in radians?

Answer 6

π/2

Question 7

What is 270 degrees in radians?

Answer 7

3π/2

Question 8

What is 60 degrees in radians?

Answer 8

π/3

Question 9

What is 45 degrees in radians?

Answer 9

π/4

Question 10

What is 30 degrees in radians?

Answer 10

π/6

Question 11

What is 120 degrees in radians?

Answer 11

90 deg + 30 deg
π/2 + π/6
3π/6 + π/6
4π/6
2π/3 radians

Question 12

What is the equation for arclength (S)?

Answer 12

S = rθ, where r is the radius of the circle and θ is the angle in radians

Question 13

For a circle with radius 4, find the length of a 60 degree arc.

Answer 13

S = rθ
θ = 60 degrees = π/3 radians
S = 4(π/3)
S = 4π/3