4.2 Highlights

Question 1

___ are a unit of measurement for angles such that __ ___ correspond to a rotation through an entire unit circle

Answer 1

radians

2pi radians

Question 2

Converting radians to degrees

Answer 2

θ radians = [ (180θ)/π ] °

Question 3

Converting degrees to radians

Answer 3

θ° = [ (θπ)/180 ] radians

Question 4

Radius corresponding to an angle for θ>0

Answer 4

the radius of the unit circle corresponding to θ radians is the radius that has angle θ radians with the positive horizontal axis, as measured counterclockwise from the positive horizontal axis

Question 5

Radius corresponding to a negative angle, θ<0

Answer 5

the radius that has angle |θ| radians with the positive horizontal axis, as measured from the positive horizontal axis

Question 6

A radius of the unit circle corresponding to θ radians also corresponds to __ radians for every integer n

Answer 6

θ + 2πn

Question 7

Length of a circular arc:

if 0 < θ ≤ 2π, then a circular arc on the unit circle corresponding to θ radians has length __

Answer 7

θ

Question 8

Area of a slice with angle θ radians inside a circle of radius r has the area:

Answer 8

1/2 * θ * r^2

Question 9

Special points on the unit circle: 
0 radians 
π/6 radians
π/4 radians 
π/3 radians
π/2 radians
π radians

Answer 9

0 radians: (1,0)
π/6 radians: (√3/2, 1/2)
π/4 radians: (√2/2, √2/2)
π/3 radians: (1/2, √3/2)
π/2 radians: (0,1) 
π radians: (-1,0) 

alternatively:
0 radians: (1,0)
π/2 radians: (0,1)
π radians: (-1,0)

π/6 radians: (√3/2, 1/2)
π/3 radians: (1/2, √3/2)

π/4 radians: (√2/2, √2/2)