Common Core · High school
HSG-C.B.5
High school — Derive the fact that arc length and sector area are proportional to the radius, and define radian measure.
High school — Derive the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle.
High school — Derive arc length and sector area as proportional to the radius, and define radian measure from it.
The 3 skills that cover it
- CirclesUse radius, diameter, circumference and area, and work with arcs and sectors.Read the lesson →
- Angles & Segments in CirclesRelate the angles and segments inside and around a circle: central and inscribed angles, chords, tangents and secants, and the products of the segments they cut.Read the lesson →
- Radians & DegreesMeasure angles by arc length instead of by 360ths of a turn, and convert between radians and degrees.Read the lesson →
What a student should be able to do
- Convert between radius and diameter.
- Compute circumference and area of a circle.
- Find an arc length and a sector area.
- Work backwards from circumference or area to the radius.
- Find an inscribed angle from its arc or central angle, including angles in a semicircle.
- Use the properties of chords, tangents and the tangent-radius right angle.
- Find angles formed by chords, secants and tangents meeting inside or outside the circle.
- Use the chord, secant and tangent segment products to find an unknown length.
- Convert degrees to radians and back.
- Explain why a full turn is 2*pi radians.
- Find arc length and sector area using radians.
- Recognise the common radian measures on sight.