Sin usar calculadora, oblén el valor nimerico de

Ask by Williams Carlson. in Ecuador

Jan 20,2025

Question

Sin usar calculadora, oblén el valor nimerico de $$ 3 	an \frac{\pi}{6} \operatorname{sen} \frac{\pi}{3} $$

UpStudy AI · Accepted Answer

Para calcular el valor numérico de $$ 3 \tan \frac{\pi}{6} \sin \frac{\pi}{3} $$ sin usar una calculadora, seguimos estos pasos:

1. **Calcular $$ \tan \frac{\pi}{6} $$:**

Sabemos que:
   $$
   \tan \frac{\pi}{6} = \tan 30^\circ = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}
   $$

2. **Calcular $$ \sin \frac{\pi}{3} $$:**

Sabemos que:
   $$
   \sin \frac{\pi}{3} = \sin 60^\circ = \frac{\sqrt{3}}{2}
   $$

3. **Sustituir los valores en la expresión original:**
   $$
   3 \tan \frac{\pi}{6} \sin \frac{\pi}{3} = 3 \left( \frac{\sqrt{3}}{3} \right) \left( \frac{\sqrt{3}}{2} \right)
   $$

4. **Simplificar la expresión:**
   $$
   3 \left( \frac{\sqrt{3}}{3} \right) \left( \frac{\sqrt{3}}{2} \right) = 3 \times \frac{\sqrt{3} \times \sqrt{3}}{3 \times 2}
   $$
   $$
   = 3 \times \frac{3}{6} = 3 \times \frac{1}{2} = \frac{3}{2}
   $$

**Resultado final:**
$$
3 \tan \frac{\pi}{6} \sin \frac{\pi}{3} = \frac{3}{2}
$$
The value is $$ \frac{3}{2} $$.

Sin usar calculadora, oblén el valor nimerico de

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