Pregunta
Find the evact vatue of \( \sec 30^{\circ} \). \( \sec 30^{\circ}=\square \) (Simplify your answec including any radicals. Use integers or fractions for any numbers in the expression.)
Ask by Blake Norton. in the United States
Mar 13,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\[
\sec 30^\circ = \frac{2\sqrt{3}}{3}
\]
Solución
1. Recall the definition:
\[
\sec 30^\circ = \frac{1}{\cos 30^\circ}
\]
2. The cosine of \(30^\circ\) is known:
\[
\cos 30^\circ = \frac{\sqrt{3}}{2}
\]
3. Substitute the value of \(\cos 30^\circ\) into the formula:
\[
\sec 30^\circ = \frac{1}{\frac{\sqrt{3}}{2}} = \frac{2}{\sqrt{3}}
\]
4. Rationalize the denominator to write the expression in simplest form:
\[
\frac{2}{\sqrt{3}} = \frac{2\sqrt{3}}{3}
\]
Thus,
\[
\sec 30^\circ = \frac{2\sqrt{3}}{3}
\]
Respondido por UpStudy AI y revisado por un tutor profesional
Como
error msg
Explicar 
Simplifique esta solución Extra Insights
To find the exact value of \( \sec 30^{\circ} \), we start by remembering that the secant function is the reciprocal of the cosine function. Therefore, we have: \[ \sec 30^{\circ} = \frac{1}{\cos 30^{\circ}} \] We know from trigonometric values that \( \cos 30^{\circ} = \frac{\sqrt{3}}{2} \). So now we can plug this value into the equation: \[ \sec 30^{\circ} = \frac{1}{\frac{\sqrt{3}}{2}} = \frac{2}{\sqrt{3}} \] To express this in a simplified form, we can multiply the numerator and the denominator by \( \sqrt{3} \): \[ \sec 30^{\circ} = \frac{2\sqrt{3}}{3} \] So, the exact value of \( \sec 30^{\circ} \) is: \[ \sec 30^{\circ} = \frac{2\sqrt{3}}{3} \]
¡Prueba Premium ahora!
¡Prueba Premium y hazle a Thoth AI preguntas de matemáticas ilimitadas ahora!
Quizas mas tarde
Hazte Premium
