Problem

What is the value of $\sec \left(334^{\circ} 10^{\prime}\right)$ to the nearest hundredth?

Answer

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Answer

So, \[\frac{1}{\cos (334^\circ 10^\prime)} \approx \boxed{1.12}.\]

Steps

Step 1 ：We have that \[\sec (334^\circ 10^\prime) = \frac{1}{\cos (334^\circ 10^\prime)}.\]

Step 2 ：Since the cosine function has period $360^\circ,$

Step 3 ：\[\cos (334^\circ 10^\prime) = \cos (334^\circ 10^\prime - 360^\circ) = \cos (-25^\circ 50^\prime).\]

Step 4 ：Converting to decimal degrees, we get \[-25^\circ 50^\prime = -25.8333^\circ.\]

Step 5 ：Using the cosine function, we find that \[\cos (-25.8333^\circ) \approx 0.8910.\]

Step 6 ：So, \[\frac{1}{\cos (334^\circ 10^\prime)} \approx \boxed{1.12}.\]

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