Pregunta
\( 1 \leftarrow \quad \) Find a value of \( \alpha \) in the interval \( \left[0^{\circ}, 90^{\circ}\right] \) that satisfies the given statement. \( \cot \alpha=1.2199536 \)
Ask by Summers Bolton. in the United States
Mar 13,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\( \alpha \approx 39.5^{\circ} \)
Solución
Let's calculate \( \alpha \) using the arctangent function:
1. Calculate \( \alpha \):
\[
\alpha \approx \tan^{-1}(0.819)
\]
Using a calculator or a trigonometric table, we find:
\[
\alpha \approx 39.5^{\circ}
\]
Thus, the value of \( \alpha \) that satisfies \( \cot \alpha = 1.2199536 \) in the interval \( [0^{\circ}, 90^{\circ}] \) is approximately:
\[
\alpha \approx 39.5^{\circ}
\]
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg
Explicar 
Simplifique esta solución Extra Insights
To find the value of \( \alpha \) that satisfies \( \cot \alpha = 1.2199536 \), we can use the fact that \( \cot \alpha = \frac{1}{\tan \alpha} \). Therefore, we can find \( \tan \alpha = \frac{1}{1.2199536} \), which is approximately \( 0.819 \). Using a calculator or a trigonometric table, the angle \( \alpha \) that corresponds to a tangent value of \( 0.819 \) falls in the first quadrant. The value of \( \alpha \) is approximately \( 39.6^{\circ} \).
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
