Radian Measure and Arc Length
Aligned to F-TF.A.1 — Common Core State Standards for Mathematics.
What this lesson teaches
One radian is the angle that subtends an arc equal in length to the radius. On the unit circle (radius 1), the radian measure of an angle equals the length of the arc it cuts off, and a full circle is 2 × pi radians.
Worked example
A quarter of a circle is one fourth of 2 × pi = pi/2 radians. On the unit circle, that arc has length pi/2, which is about 1.57.
Practice questions
- How many radians are in a full circle?
- Convert 180 degrees to radians.
- On the unit circle, what arc length matches an angle of pi/3 radians?
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Medida en radianes y longitud de arco
Un radián es el ángulo que subtiende un arco de longitud igual al radio. En el círculo unitario (radio 1), la medida en radianes de un ángulo es igual a la longitud del arco que abarca, y una circunferencia completa mide 2 × pi radianes.
Ejemplo: Un cuarto de circunferencia es la cuarta parte de 2 × pi = pi/2 radianes. En el círculo unitario, ese arco tiene longitud pi/2, aproximadamente 1.57.
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