Unit 7, Lesson 16
Radian Sense
Integrated Math 2
16.1
Warm-up
Which three go together? Why do they go together?
A
B
C
D
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Which three go together? Why do they go together?
A
B
C
D
This double number line shows measures in degrees on one line and in radians on another.
radians
radians
30
120
Your teacher will give you a set of cards with angle measures on them. Place the cards upside down in a pile. Take turns with your partner drawing a card.
| card | measure in radians (may be blank) | total shaded, in radians |
|---|---|---|
| card | measure in radians (may be blank) | total shaded, in radians |
|---|---|---|
When you’re finished, answer these questions about each circle:
We can divide circles into congruent sectors to get a sense for the size of an angle measured in radians.
Suppose we want to draw an angle that measures radians. We know that radians is equivalent to 180 degrees. If we divide a sector with a central angle of radians into thirds, we can shade in two of the sectors to create an angle measuring radians.
Another way to understand the size of an angle measured in radians is to create a double number line with degrees on one line and radians on the other. On the double number line shown here, the degree measures are aligned with their equivalent radian measures. For example, radians is equivalent to 180.
Suppose we need to know the size of an angle that measures radians. The left half of the double number line represents radians. Divide the left half of the top and bottom number lines into fourths, then count out 3 of them on the radians line to land on . On the top line, each interval we drew represents 45 degrees because . If we count 3 of those intervals, we find that radians is equivalent to 135 degrees because .