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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 1
Capitolo 3, Problema 1

Match each trigonometric function in Column I with its value in Column II. Choices may be used once, more than once, or not at all.

sin 30°

Guida verificata passo dopo passo
1
Recall the definition of the sine function for an angle in degrees: \(\sin \theta\) represents the ratio of the length of the side opposite the angle \(\theta\) to the hypotenuse in a right triangle.
Identify the angle given in the problem, which is \(30^\circ\).
Use the known exact value of \(\sin 30^\circ\), which is a standard angle in trigonometry.
Recall or refer to the unit circle or special right triangles (like the 30°-60°-90° triangle) to find that \(\sin 30^\circ = \frac{1}{2}\).
Match \(\sin 30^\circ\) with the value \(\frac{1}{2}\) in Column II.

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Basic Trigonometric Ratios

Trigonometric functions like sine, cosine, and tangent relate the angles of a right triangle to the ratios of its sides. Specifically, sine of an angle is the ratio of the length of the opposite side to the hypotenuse. Understanding these ratios is fundamental to evaluating functions such as sin 30°.
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Introduction to Trigonometric Functions

Special Angles and Their Values

Certain angles, such as 30°, 45°, and 60°, have well-known exact trigonometric values. For example, sin 30° equals 1/2. Memorizing these special angle values helps quickly solve problems without a calculator and is essential for matching functions to their values.
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45-45-90 Triangles

Function-Value Matching in Trigonometry

Matching trigonometric functions to their numerical values involves recognizing the function's definition and recalling or calculating its value at specific angles. This skill is important for solving problems where functions must be paired with correct values, often using known angle measures.
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Introduction to Trigonometric Functions
Pratica correlata
Domanda del libro di testo

CONCEPT PREVIEW Match each trigonometric function value or angle in Column I with its appropriate approximation in Column II.

Column I: 1. sin 83°

Column II: A. 88.09084757°; B. 63.25631605°; C. 1.909152433°; D. 17.45760312°; E. 0.2867453858; F. 1.962610506; G. 14.47751219°; H. 1.015426612; I. 1.051462224; J. 0.9925461516

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Domanda del libro di testo

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.

cot(90°-4.72°)

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Domanda del libro di testo

(Modeling) Grade Resistance Solve each problem. See Example 3. Find the grade resistance, to the nearest ten pounds, for a 2400-lb car traveling on a -2.4° downhill grade.

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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.

sec θ = 1.1606249

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