Chapter 4-1: Radian Measure & 4.4: Angles Page 1 of 12

Part 1: Chapter 4.1: Radian Measure

360°

2π

2𝜋 = 360°

𝜋 = 180°

Converting between Radians and Degrees…

…Set up a proportion and solve for the missing

value…

𝜋

𝑥 =

180°

50°

Chapter 4-1: Radian Measure & 4.4: Angles Page 2 of 12

Example 2: Convert 270° to radians…

Example 3: Convert 𝜋

6 radians to degrees….

Chapter 4-1: Radian Measure & 4.4: Angles Page 3 of 12

𝜃 = 0

𝜃 = 2𝜋

𝜃 =

𝜃 =

𝜃 =

Chapter 4-1: Radian Measure & 4.4: Angles Page 4 of 12

Chapter 4-1: Radian Measure & 4.4: Angles Page 5 of 12

Part 2: Chapter 4.4: Angles:

Coterminal angles are angles in standard position (angles with

the initial side on the positive x-axis) that have a common

terminal side.

To find a positive and a negative angle coterminal with a

given angle, you can add and subtract 360° if the angle is

measured in degrees or 2π if the angle is measured

in radians.

Chapter 4-1: Radian Measure & 4.4: Angles Page 6 of 12

For example 30°, –330° and 390° are all coterminal.

Chapter 4-1: Radian Measure & 4.4: Angles Page 7 of 12

In Radians…

For the positive angle,

subtract 2 to obtain a

coterminal angle.

For the negative angle,

add 2 to obtain a

coterminal angle.

Chapter 4-1: Radian Measure & 4.4: Angles Page 8 of 12

Example 1:

Find a positive and a negative

angle coterminal with a 55°

angle.

Example 2:

Find a positive and a negative

angle coterminal with a 𝜋

3 angle.

initial side

y

x initial side

y

x

Chapter 4-1: Radian Measure & 4.4: Angles Page 9 of 12

Reference Angles…

180° − 𝑎𝑛𝑔𝑙𝑒 = 𝜃

𝑎𝑛𝑔𝑙𝑒 − 180° = 𝜃

360° − 𝑎𝑛𝑔𝑙𝑒 = 𝜃

Chapter 4-1: Radian Measure & 4.4: Angles Page 10 of 12

Example: Find the reference angle & the coterminal

angle

Chapter 4-1: Radian Measure & 4.4: Angles Page 11 of 12

Example: Find the reference angle & the coterminal

angle

Chapter 4-1: Radian Measure & 4.4: Angles Page 12 of 12

Example: Find the reference angle & the coterminal

angle