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Chapter 4: Problem 36

Use a calculator to evaluate each function. Round your answers to four decimal places. (Be sure the calculator is in the correct mode.) (a) sec \(42^{\circ} 12^{\prime}\) (b) \(\csc 48^{\circ} 7^{\prime}\)

Short Answer

Expert verified
The value of function (a) sec \(42^{\circ} 12^{\prime}\) will be obtained after you have calculated cos\(42.2^{\circ}\) and found the reciprocal. This process will also apply to function (b) \( \csc{48^{\circ} 7^{\prime}} \) but with sin instead of cos. The exact values, however, will vary depending on the specific calculator used, and after rounding to four decimal places.

Step by step solution

01

Conversion to Decimal Degrees

First, convert degrees and minutes into decimal degrees. 1 degree has 60 minutes. Therefore, for (a) \( 42^{\circ} 12^{\prime} = 42 + \frac{12}{60} = 42.2 ^{\circ} \) and for (b) \( 48^{\circ} 7^{\prime} = 48 + \frac{7}{60} = 48.1167 ^{\circ} \). Now that we have the angles in decimal degrees, we can input these into our equations.
02

Calculation of Trigonometric Functions using Calculator

Sec and Csc are reciprocal of Cos and Sin, respectively. Therefore, calculate the value of cos and sin for the given angles, then take the reciprocal. It's important to assure the calculator is in degree mode. (a) To find sec \( 42.2^{\circ} \), first calculate cos \( 42.2^{\circ} \) and then find its reciprocal. (b) For calculating \( \csc{48.1167^{\circ}} \), first calculate sin \( 48.1167^{\circ} \) then find its reciprocal.
03

Rounding the Answer

After calculating the values, round your answer to the fourth decimal place. Make sure to round correctly, if the digit at the fifth place is 5 or more, round up the fourth digit.

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Most popular questions from this chapter

A carousel with a 50 -foot diameter makes 4 revolutions per minute. (a) Find the angular speed of the carousel in radians per minute. (b) Find the linear speed (in feet per minute) of the platform rim of the carousel.

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