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8.- Dado Sen \( B=0.1938 \) ¿Cuál es el valor numérico de \( \operatorname{Cot} B \) ?

Ask by Ramos Gray. in Mexico
Feb 19,2025

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El valor numérico de cot B es aproximadamente 5.063.

Solución

Dado que sin B = 0.1938, recordamos que la cotangente se define como:   cot B = cos B / sin B Para hallar cos B, usamos la identidad pitagórica:   sin² B + cos² B = 1   cos² B = 1 − sin² B Calculamos sin² B:   sin² B = (0.1938)² ≈ 0.03757 Luego:   cos B = √(1 − 0.03757) ≈ √0.96243 ≈ 0.9811 Ahora, sustituimos en la definición de cotangente:   cot B = 0.9811 / 0.1938 ≈ 5.063 Por lo tanto, el valor numérico de cot B es aproximadamente 5.063.

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Para encontrar el valor de \( \operatorname{Cot} B \), utilizamos la relación que \( \operatorname{Cot} B = \frac{1}{\operatorname{Tan} B} \). Primero, calculamos \( \operatorname{Tan} B \): \[ \operatorname{Tan} B = \tan(0.1938) \approx 0.1953 \] Ahora, calculamos \( \operatorname{Cot} B \): \[ \operatorname{Cot} B = \frac{1}{\operatorname{Tan} B} \approx \frac{1}{0.1953} \approx 5.12 \] Así que el valor numérico de \( \operatorname{Cot} B \) es aproximadamente 5.12.

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