Skip to main content
Ch. 2 - Acute Angles and Right Triangles
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLial 12th EditionCh. 2 - Acute Angles and Right TrianglesProblema 2.3.22
Capitolo 3, Problema 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°

Guida verificata passo dopo passo
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.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
2m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

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.
Video consigliato:
Percorso guidato
6:22
Graphs of Secant and Cosecant Functions

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.
Video consigliato:
Percorso guidato
6:36
Simplifying Trig Expressions

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.
Video consigliato:
Percorso guidato
4:45
How to Use a Calculator for Trig Functions
Pratica correlata
Domanda del libro di testo

(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.

689
views
Domanda del libro di testo

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°

628
views
Domanda del libro di testo

(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.

655
views
Domanda del libro di testo

Solve each problem. See Examples 1 and 2. Distance Traveled by a Ship A ship travels 55 km on a bearing of 27° and then travels on a bearing of 117° for 140 km. Find the distance from the starting point to the ending point.

940
views
Domanda del libro di testo

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

641
views
Domanda del libro di testo

Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2.

sin θ = 0.84802194

692
views