*Definition of a Radian

Today we are going to learn about another angle measurement, called the [b][i]radian.[br][/i][/b]Follow the directions below the applet and answer the questions as you go along.[br][i]Click the refresh button in the top right corner of the applet to get started.[/i]

1. What is the length of the radius of the circle?[br] [i] Questions will get a bit harder as we go :)[/i]

Move point B so it is the arc s is the same length as the radius. Get it as close as you can.

2. How many degrees is the angle that you made with an arc length equal to its radius? [i] Also notice the radian measurement.[/i]

Move point B so that the arc length "s" is twice the length of the radius.

3. How many degrees is the angle now? [i] Also notice the radian measurement.[/i]

Check the box next to "Show Text 1"

4. Describe what a radian is in your own words.

Check the box next to "Show Text 2." Then, adjust the radius slider to increase the size of the radius.

5. Does this change the radian measure of the angle?

6. How many degrees are in a semi-circle?

Adjust B so the angle is equal to the semi-circle.

7. How many radians are in a semi-circle?

Predict...

8. How many radians are in a full circle? (Check your answer by changing where B is)

Converting Between Radians and Degrees

We use conversions to go between degrees and radians. Because radians is usually given in terms of [math]\pi[/math], we use [math]\pi[/math] in the conversion.

What conversion would you use that has [math]\pi[/math] in it?[br][br]______ degrees = ______[math]\pi[/math]_ radians

[center]Convert the following degree measurements to radians. [br][i]Your answer should be a simplified fraction in terms of [/i][math]\pi[/math][i]. [/i] [/center][center] [math]30^\circ[/math][/center]

[math]\frac{\pi}{6}[/math] answer not given [math]120\pi[/math] [math]\frac{\pi}{3}[/math] [math]\frac{\pi}{5}[/math]

[center]Convert the following degree measurements to radians. [br][i]Your answer should be a simplified fraction in terms of [/i][math]\pi[/math][i]. [/i] [/center][center] [math]160^{\circ}[/math][/center]

[math]\frac{9\pi}{8}[/math] [math]\frac{4\pi}{9}[/math] answer not given [math]\frac{8\pi}{9}[/math] [math]\frac{9\pi}{4}[/math]

[center]Convert the following degree measurements to radians. [br][i]Your answer should be a simplified fraction in terms of [/i][math]\pi[/math][i]. [/i] [/center][center] [math]200^{\circ}[/math][/center]

[math]\frac{9\pi}{5}[/math] [math]\frac{5\pi}{9}[/math] answer not given [math]\frac{10\pi}{9}[/math] [math]\frac{9\pi}{10}[/math]

[center]Convert the following degree measurements to radians. [br][i]Your answer should be a simplified fraction in terms of [/i][math]\pi[/math][i]. [/i] [/center][center] [math]225^{\circ}[/math][/center]

answer not given [math]\frac{5\pi}{8}[/math] [math]\frac{7\pi}{4}[/math] [math]\frac{8\pi}{5}[/math] [math]\frac{4\pi}{7}[/math]

[center]Convert the following radian measurements to degrees. [i] [/i] [/center][center] [math]\frac{2\pi}{5}[/math][/center]

answer not given [math]450^\circ[/math] [math]144^\circ[/math] [math]900^\circ[/math] [math]72^\circ[/math]

[center]Convert the following radian measurements to degrees. [i] [/i] [/center][center] [math]3\pi[/math][/center]

[math]450^\circ[/math] [math]540^{\circ}[/math] [math]90^\circ[/math] answer not given [math]-180^{\circ}[/math]

[center]Convert the following radian measurements to degrees. [i] [/i] [/center][center] [math]\frac{3\pi}{4}[/math][/center]

[math]225^{\circ}[/math] [math]45^{\circ}[/math] answer not given [math]135^{\circ}[/math] [math]315^{\circ}[/math]

If you have time....

#1: What is the radian measure of the angle formed by the hands of a clock at 2:00 p.m.? (Stuck? To think about: How many hours are there on a clock face? So how many equal size pieces are we breaking the clock face into?) [br][br]

π/2 π/6 π/3 π/4

#2: Through how many radians does the minute hand of a clock turn in 24 minutes? [br]

0.4π 0.8π 0.2π 0.6π