# ATL (Criteria B): Exploring Radians and Degrees

Topic:
Angles

## Slowly move the "Change Angle" slider all the way to the right until the entire circumference has been traced.

1) How many different colors arc lengths are formed?

Select all that apply
• A
• B
• C

## 2) One arc represents one radian.

You may drag the radius slider to change the length of the radius. What did you observe about the length of one arc and the length of the radius?

﻿The length of one arc ______ to the length of the radius.

Select all that apply
• A
• B
• C

## Now, make sure the diagram is a unit circle, i.e. r = 1.

3) How many radians are in a circle? (HINT: How many arcs is formed for a circle.)

## Next, determine the degrees formed by one arc length (which is 1 radian).

- Select the "angle" tool in the upper left-hand corner. - Select one of the endpoints, the center, and the other endpoints.

## 4) How many degrees are in 1 radian?

[Hint: supposed to be an acute angle.]

## 5) Combine Q2 & Q4.

You mentioned that there are x radians in a circle (in Q2) and 1 radian= y degrees in Q4. What can you conclude from these two pieces of information?

## 6) Suggest next pattern.

Suggest how I should calculate the length of 2 colored arcs of a circle with a radius of 3.0. [Reminder: Explain the process instead of the final answer.]

## 7) Suggest a general rule.

Suggest how I should calculate the length of an arc of a circle, s with a radius of r where the arc formed an angle of radian. Write a formula relate s, r, .