Question

question given sec a = 41/9 and that angle a is in quadrant i, find the exact value of sin a in simplest radical form using a rational denominator. answer attempt 1 out of 2

Explanation:

Step1: Recall the identity

We know that \(\sec A=\frac{1}{\cos A}\), so if \(\sec A = \frac{41}{9}\), then \(\cos A=\frac{9}{41}\).

Step2: Use the Pythagorean identity

The Pythagorean identity is \(\sin^{2}A+\cos^{2}A = 1\). Substitute \(\cos A=\frac{9}{41}\) into the identity: \(\sin^{2}A=1-\cos^{2}A\).

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Step3: Determine the sign of \(\sin A\)

Since angle \(A\) is in Quadrant I, \(\sin A>0\). So \(\sin A=\sqrt{\frac{1600}{1681}}=\frac{40}{41}\)

Answer:

\(\frac{40}{41}\)