Warm-Up

The infield of a baseball field is a square.
The distance from home plate to first
base is 90 feet.
◦ What is the distance from home plate to
second base?
◦ What is the distance from third base to first
base?
◦ What is the distance to the pitcher’s mound if
it is equidistant from all the bases?
Radian/Degree Conversions
A love story
Learning Outcomes

I will be able to discuss angle measures in
terms of degrees or radians

I will be able to convert between radians
and degrees

I will be able to fill in a unit circle for both
degrees and radians.
What are radians?

Radians are a way to measure angles as
the distance around a unit circle.

What is a unit circle?

A unit circle is a circle with a radius of 1.
Why do we use radians?

We use radians because at higher levels of
math, radians are much easier to use for
functions when compared to degrees.
How do we use radians?
Suppose we have a unit circle. What is the
distance around the circle?
C = 2πr
or in the case of a unit circle C = 2π


Well what is the distance around a circle
in degrees?
360°
How do we use radians?

This means that our conversion factor
looks like this…
2𝜋
360

or if we simplify
𝜋
180
We can use this to create an equation for
finding radians or degrees.
rad = deg ∙
𝜋
180
deg = rad ∙
180
𝜋
How do we use radians?

Let’s try to convert degrees to radians.
90°
60°
40°
270°
Remember:
rad = deg ∙
rad = 90° ∙
rad =
𝜋
2
𝜋
180
𝜋
180
rad = deg ∙
rad = deg ∙
rad = 60° ∙
rad =
𝜋
3
𝜋
180
𝜋
180
𝜋
180
rad = deg ∙
rad = 40° ∙
rad =
2𝜋
9
𝜋
180
𝜋
180
rad = deg ∙
𝜋
180
rad = 270° ∙
𝜋
180
rad =
3𝜋
2
How do we use radians?

Let’s try to convert radians to degrees.
𝜋
4
𝜋
6
Remember:
deg =
deg =
180
rad ∙
𝜋
𝜋 180
∙
4
𝜋
deg = 45º
deg =
deg =
2𝜋
5
4𝜋
3
deg = rad ∙
180
rad ∙
𝜋
𝜋 180
∙
6
𝜋
deg = 30º
deg =
deg =
180
𝜋
180
rad ∙
𝜋
2𝜋 180
∙
5
𝜋
deg = 72º
deg =
deg =
180
rad ∙
𝜋
4𝜋 180
∙
3
𝜋
deg = 240º
Think Radians Worksheet
The Unit Circle

What is a unit circle?

A unit circle is a circle with a radius of 1.

If our goal is to find coordinates of the
unit circle what information might we be
able to use?
The Unit Circle
1
y
x
Exit Ticket


Convert 45º to
radians.
Convert
degrees.
𝜋
5
Homework

Finish Think Radians
Worksheet and Blank
Unit Circle

QUIZ NEXT
CLASS!!!
to