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
- What are sine and cosine of 0°?
- On the unit circle, what coordinate gives the cosine?
- 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 lessonEn 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).
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