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Ch. 2 - Acute Angles and Right Triangles
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook
All textbooksLial 12th EditionCh. 2 - Acute Angles and Right TrianglesProblem 2.3.22
Chapter 3, Problem 2.3.22

Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1.
1/ sec 14.8°

Verified step by step guidance
1
Recall the definition of the secant function: \(\sec \theta = \frac{1}{\cos \theta}\). This means that \(\frac{1}{\sec \theta} = \cos \theta\).
Rewrite the given expression \(\frac{1}{\sec 14.8^\circ}\) as \(\cos 14.8^\circ\) using the identity from step 1.
Use a calculator to find the value of \(\cos 14.8^\circ\). Make sure your calculator is set to degree mode since the angle is given in degrees.
Calculate the cosine value and round the result to six decimal places as requested.
Write down the final answer with six decimal places, ensuring the approximation is clear and precise.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Understanding the Secant Function

The secant function, sec(θ), is the reciprocal of the cosine function, defined as sec(θ) = 1/cos(θ). Knowing this relationship allows you to rewrite expressions involving secant in terms of cosine, which is often easier to evaluate using a calculator.
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Simplifying Trigonometric Expressions

Simplifying expressions before calculation helps reduce errors and makes the evaluation process straightforward. For example, rewriting 1/sec(θ) as cos(θ) simplifies the expression and avoids dealing with complex reciprocal values directly.
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Using a Calculator for Trigonometric Values

Calculators typically provide trigonometric functions like sine, cosine, and tangent. To find values like cos(14.8°), ensure the calculator is set to degree mode, input the angle correctly, and round the result to the required decimal places for precision.
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Related Practice
Textbook Question

Solve each problem. See Examples 1 and 2. Distance between Two Cities The bearing from Atlanta to Macon is S 27° E, and the bearing from Macon to Augusta is N 63° E. An automobile traveling at 62 mph needs 1¼ hr to go from Atlanta to Macon and 1¾ hr to go from Macon to Augusta. Find the distance from Atlanta to Augusta.

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(Modeling) Grade Resistance Solve each problem. See Example 3. A 3000-lb car traveling uphill has a grade resistance of 150 lb. Find the angle of the grade to the nearest tenth of a degree.

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Use a calculator to determine whether each statement is true or false. A true statement may lead to results that differ in the last decimal place due to rounding error. sin 10° + sin 10° = sin 20°

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Textbook Question

(Modeling) Grade Resistance Solve each problem. See Example 3. A car traveling on a -3° downhill grade has a grade resistance of -145 lb. Determine the weight of the car to the nearest hundred pounds.

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Textbook Question

Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1.

sin 38° 42'

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Textbook Question

Find two angles in the interval [0°, 360°) that satisfy each of the following. Round answers to the nearest degree. sin θ = 0.52991926

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