CurriculumGrade 12Mathematics

Trigonometric Functions and the Unit Circle

Aligned to F-TF.A.2 — Common Core State Standards for Mathematics.

What this lesson teaches

On the unit circle (radius 1), the cosine of an angle is the x-coordinate and the sine is the y-coordinate. This extends trig to all angles, not just those in right triangles.

Worked example

At 90° the point is (0, 1), so cos(90°) = 0 and sin(90°) = 1. At 0° the point is (1, 0).

Practice questions

  1. What are sine and cosine of 0°?
  2. On the unit circle, what coordinate gives the cosine?
  3. Find sin(180°) using the unit circle.

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 lesson

En español

Funciones Trigonométricas y el Círculo Unitario

En el círculo unitario (radio 1), el coseno de un ángulo es la coordenada x y el seno es la coordenada y. Esto extiende la trigonometría a todos los ángulos, no solo a los de los triángulos rectángulos.

Ejemplo: En 90° el punto es (0, 1), entonces cos(90°) = 0 y sin(90°) = 1. En 0° el punto es (1, 0).

More Functions lessons

Equivalent Forms of a FunctionF-IF.C.8Comparing Functions in Different FormsF-IF.C.9Building Functions from Two QuantitiesF-BF.A.1Transformations of Function GraphsF-BF.B.3Inverse FunctionsF-BF.B.4Radian Measure and Arc LengthF-TF.A.1

Teach this lesson today

An AI tutor that guides with questions instead of just giving answers — all K–12 core subjects, every child in the family.

Start free — no card required