UP:MA19.A2.34
Vocabulary
- Radian measure
- Constant of proportionality
- Unit circle
- Intercepted arc
Knowledge
Students know:
- The circumference of any circle is 2πr and therefore, the circumference of a unit circle is 2π.
Skills
Students are able to:
- Translate between arc length and central angle measures in circles.
Understanding
Students understand that:
- Radians measure angles as a ratio of the arc length to the radius.
- The unit circle has a circumference of 2π which aids in sense making for angle measure as revolutions (one whole revolution measures 2π radians) regardless of radius.
- Use of the unit circle gives a one-to-one ratio between arc length and the measure of the central angle, putting the angle in direct proportion to the arc length, and that the circle can then be divided up to find the radian measure of other angles.
Body
- Define the radian measure of an angle as the constant of proportionality of the length of an arc it intercepts to the radius of the circle; in particular, it is the length of the arc intercepted on the unit circle.
