CurriculumGrade 11Mathematics

Radian Measure of Angles

Aligned to F-TF.A.1 — Common Core State Standards for Mathematics.

What this lesson teaches

A radian is the angle that cuts off an arc equal in length to the radius. On the unit circle a full turn is 2π radians, so 180° equals π radians. Convert degrees to radians by multiplying by π/180.

Worked example

Convert 60° to radians. Multiply by π/180: 60 × π/180 = 60π/180 = π/3 radians. So a 60° angle subtends an arc of length π/3 on the unit circle.

Practice questions

  1. Convert 90° to radians.
  2. Convert π/4 radians to degrees.
  3. What arc length does an angle of π/2 subtend on the unit circle?

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Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.

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En español

Medida en Radianes de Ángulos

Un radián es el ángulo que corta un arco de longitud igual al radio. En el círculo unitario una vuelta completa es 2π radianes, así que 180° equivale a π radianes. Convierte grados a radianes multiplicando por π/180.

Ejemplo: Convierte 60° a radianes. Multiplica por π/180: 60 × π/180 = 60π/180 = π/3 radianes. Así que un ángulo de 60° subtiende un arco de longitud π/3 en el círculo unitario.

More Functions lessons

Logarithms and Exponential EquationsF-LE.A.4Graphing Key Features of FunctionsF-IF.C.7Equivalent Forms of a FunctionF-IF.C.8Building Functions from RelationshipsF-BF.A.1Transformations of GraphsF-BF.B.3Unit Circle and Trig FunctionsF-TF.A.2

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