Lecture Note (Click to open)

Video Lecture of Lecture Note

Learning Objectives:

After you complete this section, you will be able to

1. Describe degree, radian, and angle in standard position/

2. Convert degree to radian and radian to degree

3. Identify coterminal angles

4. Apply arc length, angular speed, and linear speed formulas in real-life situations.

Study Tips:

Many of you already know the notion of angles, degrees, and radians. If you are familiar with those notions, then you don't have to watch the video clips. But you need to try to solve the exercise problems combined with the video clips. You should be able to understand the lecture note. However, if you are not familiar with those notions, then you are to watch the video clips before you read the lecture note.

You are to remember arc length, angular speed, and linear speed formulas.

Video Resources and Preliminary Exercise Problems:

1. Basic Introduction into degrees and radians and converting between them

Exercise: Convert the degrees $LaTeX: 45^\circ,\:90^\circ,\:120^\circ$ and $LaTeX: 180^\circ$ into radians.

2. Converting radians to degrees

Exercise: Convert the radians $LaTeX: \frac{3\pi}{4},\:\frac{7\pi}{6},\:-\frac{3\pi}{2}$ , and $LaTeX: \frac{17\pi}{3}$ .

3. Coterminal Angles

Exercise:

1. Write two positive and two negative coterminal angles of $LaTeX: 45^\circ$ .

2. Which of the following angles are coterminal with an angle of $LaTeX: 135^\circ$ ?

$LaTeX: 185^\circ,\:495^\circ,\:-30^\circ$

3. Which of the following angles are coterminal with an angle of $LaTeX: -255^\circ$ ?

$LaTeX: 105^\circ , 45^\circ , 90^\circ$

4. Arc length formula

Exercise:

1. What is the length of the arc intercepted by an angle of $LaTeX: 15^\circ$ on a circle with radius 20 meters?

2. What is the length of the arc intercepted by an angle of $LaTeX: 210^\circ$ on a circle with a radius 2.9 ft?