- Identify and draw angles of rotation in standard position.
- Identify quadrantal angles.
- Identify co-terminal angles.
Angles of Rotation in Standard Position
Consider, for example, a game that is played with a spinner. When you spin the spinner, how far has it gone? You can answer this question in several ways. You could say something like “the spinner spun around 3 times.” This means that the spinner made 3 complete rotations, and then landed back where it started.
We can use our knowledge of graphing to represent any angle. The figure below shows an angle in what is called standard position.
Points to Consider
- How can one angle look exactly the same as another angle?
- Where might you see angles of rotation in real life?
- Plot the following angles in standard position.
- State the measure of an angle that is co-terminal with 90∘.
- Name a positive and negative angle that are co-terminal with:
- A drag racer goes around a 180 degree circular curve in a racetrack in a path of radius 120 m. Its front and back wheels have different diameters. The front wheels are 0.6 m in diameter. The rear wheels are much larger; they have a diameter of 1.8 m. The axles of both wheels are 2 m long. Which wheel has more rotations going around the curve? How many more degrees does the front wheel rotate compared to the back wheel?
- Answers will vary. Examples: 450∘, −270∘
- Answers will vary. Examples: −240∘, 480∘
- Answers will vary. Examples: −45∘, 675∘
- Answers will vary. Examples: 210∘, −510∘, 570∘
- The front wheel rotates more because it has a smaller diameter. It rotates 200 revolutions versus 66.67 revolutions for the back wheel, which is a 48,000∘ difference ((200−66.6¯)⋅360∘).