Math Problem Statement

Use a calculator to find sec(53°47') and round the answer to four decimal places.

Solution

The question is asking to find the value of sec(5347)\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 534753^\circ 47', where:

    • 5353^\circ is the degree part.
    • 4747' is the minute part.

    To convert minutes to decimal degrees: Decimal Degrees=53+4760=53+476053.7833\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)=1cos(53.7833)\sec(53.7833^\circ) = \frac{1}{\cos(53.7833^\circ)}

  3. Use a Calculator: First, calculate cos(53.7833)\cos(53.7833^\circ): cos(53.7833)0.5922\cos(53.7833^\circ) \approx 0.5922 Then, find the secant: sec(53.7833)=10.59221.6873\sec(53.7833^\circ) = \frac{1}{0.5922} \approx 1.6873

So, sec(5347)1.6873\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 534753^\circ 47'?
  3. What is the tangent of 534753^\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!

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Secant Function
Angle Conversion

Formulas

Decimal Degrees = Degrees + (Minutes / 60)
sec(θ) = 1 / cos(θ)

Theorems

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Suitable Grade Level

High School (Grades 10-12)