In Try This 1 you created a central angle where the radius, AO, of the circle is the same as the length of the subtended arc, AB. This situation defines radian measure. The measure of ∠AOB is 1 rad (radian).
You may have determined that the radius of the circle would fit about 6 times around the circumference of a circle. This would mean that one full rotation, which is 360°, would be the same as about 6 rad. In Try This 2 you will try to find a more precise value for one full rotation of a circle measured in radians.
You will test your new understanding of 1 rad by investigating whether the radius of a circle changes the measure of the central angle. You will then explore the relationship between radians and degrees.
Step 1: Open Angles in Degrees and Radians.
Step 2: Slide the angle slider to change the angle to 60°. Use the arrow keys on your keyboard to change the angle by 1° at a time. Note where 1 rad is positioned.
Step 3: Slide the radius slider to change the radius to a larger value and then to a smaller value. Did the radian measure change? Why do you think this happens?
Degree | Portion of Whole Circle | Radian Measure (in terms of π) |
Radian Measure (round to three decimal places) |
Sketch or Screen Capture |
360° | 1 | |||
180° | ||||
90° | ||||
45° | ||||
−360° | −1 | |||
−180° | ||||
−90° | ||||
−45° |
If the angle is negative, in which direction does the terminal arm rotate?
Use the relationship you found in question 4 to answer the following questions.
Degree | Radian (exact value, fraction of π) |
Sketch | Quadrant |
30° | |||
60° | |||
−120° | |||
Save your responses in your course folder.
With a partner or in a group, discuss the following questions:
If required, save a record of your discussion in your course folder.