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Chapter 4: Problem 81

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is in the correct mode.) $$\sec 72^{\circ}$$

Short Answer

Expert verified
The value of \( \sec (72^{\circ}) \) to four decimal places is approximately 3.5095.

Step by step solution

01

Setting the Calculator Mode

First, ensure that the calculator is in the correct mode, specifically in degree mode since the given angle is in degrees. This can be usually found under the settings of most scientific calculators.
02

Calculating Cosine

Calculate the cosine of the given angle. In this case, the angle is 72 degrees. Therefore, input \( 72^{\circ} \) into the calculator and calculate \(\cos (72^{\circ}) \).
03

Calculating Secant

Calculate the secant of \( 72^{\circ} \). The secant of an angle is equal to the reciprocal of the cosine of the angle. So, to calculate the secant, just take the reciprocal of the previous calculated cosine value. This can be done by using the reciprocal function (1/x) of the calculator or simply by dividing one by the cosine of the angle.
04

Rounding the Answer

Finally, round the calculated secant value to four decimal places. The method of rounding may differ on calculators. However, in most of them, it informs you the decimal places up to which your answer needs to be rounded.

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