Unit Circle and Trig Functions
Aligned to F-TF.A.2 — Common Core State Standards for Mathematics.
What this lesson teaches
On the unit circle, the point at angle θ has coordinates (cos θ, sin θ). Because angles can wind around endlessly, this lets sine and cosine be defined for every real number, not just angles in a triangle.
Worked example
Find cos and sin of 5π/6. This angle is in the second quadrant with reference angle π/6. There cosine is negative and sine positive, so cos(5π/6) = −√3/2 and sin(5π/6) = 1/2.
Practice questions
- Give the coordinates on the unit circle at angle 0.
- Find sin and cos of π (half a turn).
- In which quadrant are both sin θ and cos θ negative?
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
Círculo Unitario y Funciones Trigonométricas
En el círculo unitario, el punto en el ángulo θ tiene coordenadas (cos θ, sen θ). Como los ángulos pueden girar sin fin, esto permite definir el seno y el coseno para todo número real, no solo para ángulos de un triángulo.
Ejemplo: Encuentra cos y sen de 5π/6. Este ángulo está en el segundo cuadrante con ángulo de referencia π/6. Allí el coseno es negativo y el seno positivo, así que cos(5π/6) = −√3/2 y sen(5π/6) = 1/2.
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