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Date: ________________
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Section 4.1
Angles
(Day 1)
Today’s vocabulary:
Angle – is determined by rotating a ray (half – line) about its endpoint.
Initial side – is the starting position of the ray.
Terminal side – is the position after the rotation.
Vertex – is endpoint of the ray.
Standard position – is an angle fits in coordinate system in which the origin is the vertex and the initial
side coincides with the positive x – axis.
For example:
Positive angles – are generated by counterclockwise rotation.
Negative angles - are generated by clockwise rotation.
*Angles are labeled with Greek letters such as 𝜶 (alpha), 𝜷 (beta), and 𝜽 (theta)
as well as uppercase letters A, B, and C.
1
Definition of Radian
Measure of an angle – is determined by the amount of rotation from the initial side to the terminal side.
To define a radian, you can use a central angle of a circle, one whose vertex is the center of the
circle.
One radian (rad) is the measure of a central angle 𝜃 that intercepts an arc s equal in length to the
radius r of the circle.
𝜃=
𝑠
𝑟
where 𝜃 is measured in radians.
Conversions between Degrees and Radian
1. To convert degrees to radians,
multiply degrees by
𝜋 𝑟𝑎𝑑
180°
2. To convert radians to degrees,
180°
multiply radians by 𝜋 𝑟𝑎𝑑
* 360° = 2π rad
and
180° = π rad *
* 1° =
𝜋
180
rad
and
1 rad =
180°
𝜋
*
2
Let’s do
together:
EXAMPLE 1
Converting from Radians to Degrees
5𝜋
a. 4 rad
c. 2 rad
EXAMPLE 2
b.
d.
𝜋
10
rad
9𝜋
2
rad
Converting From Degrees to Radians
a. 135°
b. -270°
c. 540°
d. -50°
3
EXAMPLE 3
a. 240°
d.
Sketch angles in Standard form
b. 500°
𝜋
c. -50°
e.
3
YOU try:
16𝜋
9
Homework!
Rewrite each angle in radian measure as multiple of π.
1. 60°
2. 320°
3. 230°
4. 540°
4
Rewrite each angle in degree measure.
5.
𝜋
6
7. 3 radians
5𝜋
6.
3
8. -
𝜋
2
Draw an angle with the given measure in standard position.
9. 640°
10.
5𝜋
12
5
 Homework: