The question is asking to find the value of $\sec(53^\circ 47')$ and round it to four decimal places.

Steps to solve:

1. Convert Degrees and Minutes to Decimal Degrees: The angle given is $53^\circ 47'$, where:

   • $53^\circ$ is the degree part.
   • $47'$ is the minute part.

   To convert minutes to decimal degrees: $\text{Decimal Degrees} = 53^\circ + \frac{47'}{60} = 53 + \frac{47}{60} \approx 53.7833^\circ$

2. Find the Secant: The secant function is the reciprocal of the cosine function, so: $\sec(53.7833^\circ) = \frac{1}{\cos(53.7833^\circ)}$

3. Use a Calculator: First, calculate $\cos(53.7833^\circ)$: $\cos(53.7833^\circ) \approx 0.5922$ Then, find the secant: $\sec(53.7833^\circ) = \frac{1}{0.5922} \approx 1.6873$

So, $\sec(53^\circ 47') \approx 1.6873$.

Would you like further details on any steps?

Here are five related questions:

1. How do you convert degrees and minutes into radians?
2. Can you find the sine and cosine of the angle $53^\circ 47'$?
3. What is the tangent of $53^\circ 47'$?
4. How is secant related to sine and tangent?
5. Can you explain why secant is the reciprocal of cosine?

Tip: Always remember to switch your calculator to degree mode when working with degrees!