Module 4: Foundations of Trigonometry

 

In Try This 1 you explored how a radian is defined by looking at both the radius and the arc length of a circle. In Try This 2 you made the connection that one rotation of a circle is 360°, and this is equal to 2π rad. You know that

In this next example you will see how the relationship between degrees and radians can be used to convert between radians and degrees.



textbook
tip

When an angle measurement is given and there are no units written after the measurement, you can assume the units are in radians. When writing an angle measurement in degrees, the degree symbol must be included to indicate the measurement is in degrees. For example,

  • 75° indicates 75 degrees
  • 110 indicates 110 radians (rad)

Read “Example 1” on pages 168 to 169 of the textbook. Think about the following as you read:

Watch “Radians and degrees” for a summary of converting between degrees and radians. If you feel comfortable converting between degrees and radians, you can skip the video and go to Self-Check 1.

 

 

This is a play button that opens “Radians and degrees.”

Source: Khan Academy
(CC BY-NC-SA 3.0)


 

Self-Check 1

 

textbook

  1. Complete “Your Turn” on page 169 of the textbook.  Answer
  2. Complete questions 2.a., 2.b., 2.c., 4.a., 4.b., 4.c., 4.e., 6.a., 6.b., and 6.e. on page 175 of the textbook. Answer
  3. Complete question C4 on page 179 of the textbook. Answer
Did You Know?

This is a photo of a hand holding a compass.

Pixland/Thinkstock

Angles can be measured in many different units. In the military it is sometimes necessary to measure very small angles when using a compass. Mils, or angular mils, are a unit the British Army uses to measure angles. Under this system, the circle of the compass is divided into 6400 gradations called mils.

 

Each quadrant of the circle, which is 90°, is equal to 1600 mils. This means that north is at 0/6400 mils, east is at 1600 mils, south is at 3200 mils, and west is at 4800 mils. Because the divisions are smaller, readings can be more accurate.1




glossary

Add radian to your copy of Mathematics 30-1 Glossary Terms.



textbook

For help defining the glossary term, you can refer to Radian Measure or to “Link the Ideas” on page 167 of the textbook for help.

 

 

This is a play button that opens Radian Measure.

 

1 Source: Adapted from ArmyCadetForce.net