Trig Values from Special Triangles
Aligned to F-TF.A.3 — Common Core State Standards for Mathematics.
What this lesson teaches
This is a (+) advanced standard. The 45-45-90 and 30-60-90 triangles give exact trig values: their fixed side ratios let you read sine, cosine, and tangent for pi/6, pi/4, and pi/3 without a calculator.
Worked example
In a 45-45-90 triangle the two legs are equal and the hypotenuse is √2 times a leg. So sin(pi/4) = cos(pi/4) = 1/√2 = √2/2, and tan(pi/4) = 1.
Practice questions
- Use the 30-60-90 triangle to find cos(pi/3).
- Find sin(pi/6) and tan(pi/6).
- Explain why tan(pi/4) = 1.
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
Valores trigonométricos con triángulos especiales
Este es un estándar avanzado (+). Los triángulos 45-45-90 y 30-60-90 dan valores trigonométricos exactos: sus razones de lados fijas permiten leer el seno, el coseno y la tangente de pi/6, pi/4 y pi/3 sin calculadora.
Ejemplo: En un triángulo 45-45-90 los dos catetos son iguales y la hipotenusa mide √2 veces un cateto. Entonces sin(pi/4) = cos(pi/4) = 1/√2 = √2/2, y tan(pi/4) = 1.
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