Lesson 1
1. Lesson 1
1.10. Explore 6
Module 6: Sinusoidal Functions
protractor: iStockphoto/Thinkstock, clock: Stockbyte/Thinkstock
In Try This 4, you may have noticed that because there are 360° in a circle and 60 min in one rotation of the minute hand, the minute hand passes through 
per minute or, equivalently, 5 min represents 30°.
In general, angles larger than 360° can be treated the same as smaller angles. Converting between radians and degrees follows the same procedure as the one used in Try This 3. In question 2.c. of Try This 4, you were asked to determine what time it was after the minute hand travelled through 5π. You know that each rotation is 2π; therefore, 5π would be 2.5 rotations, or 150 min.
Read “Example 4” on pages 487 and 488 of your textbook to see two methods of comparing the size of angles. Similar to Try This 4, one textbook solution uses the clock to help visualize the angles. Which of the two solutions shown in the textbook do you prefer?
Self-Check 3
- Complete “Your Turn” on page 488 of your textbook. Answers
- Complete questions 4, 5, 6, 8.a., and 8.c. on page 490 of your textbook. Answers
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.
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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.
Add radian to your copy of Glossary Terms.