part 1: chapter 4.1: radian...
TRANSCRIPT
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