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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 2.3.25
Capitolo 3, Problema 2.3.25

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°)

Guida verificata passo dopo passo
1
Recall the co-function identity for cotangent: \(\cot(90^\circ - \theta) = \tan(\theta)\).
Apply this identity to the given expression: \(\cot(90^\circ - 4.72^\circ) = \tan(4.72^\circ)\).
Use a calculator to find the value of \(\tan(4.72^\circ)\). Make sure your calculator is set to degree mode.
Calculate the tangent value and round the result to six decimal places.
Write the final answer as the approximate value of \(\cot(90^\circ - 4.72^\circ)\) rounded to six decimal places.

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Cotangent and Its Definition

Cotangent (cot) is a trigonometric function defined as the ratio of the adjacent side to the opposite side in a right triangle, or equivalently, cot(θ) = 1/tan(θ). Understanding cotangent helps in evaluating expressions involving cotangent values.
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Percorso guidato
5:37
Introduction to Cotangent Graph

Complementary Angle Identity

The complementary angle identity states that cot(90° - θ) = tan(θ). This identity allows simplification of cotangent expressions involving angles subtracted from 90°, making calculations easier by converting cotangent to tangent.
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Percorso guidato
3:35
Intro to Complementary & Supplementary Angles

Using a Calculator for Trigonometric Approximations

Calculators can approximate trigonometric values to a desired decimal precision. After simplifying expressions using identities, input the angle in degrees and use the calculator’s tangent function to find the value, rounding the result to six decimal places as required.
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4:45
How to Use a Calculator for Trig Functions
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CONCEPT PREVIEW Match the measure of bearing in Column I with the appropriate graph in Column II.

I. N 70° W


II. 1. A. B. C. 2. 3. 4. D. E. F. 5. N 70° W 6. 7. G. H. 8. 9. 10. I. J.

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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:

cos⁻¹ 0.45

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

CONCEPT PREVIEW Match the measure of bearing in Column I with the appropriate graph in Column II.

I. 10. N 70° E


II. 1. A. B. C. 2. 3. 4. D. E. F. 5. 6. 7. G. H. 8. 9. I. J.

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Domanda del libro di testo

Solve each problem. See Examples 3 and 4. Distance through a Tunnel A tunnel is to be built from point A to point B. Both A and B are visible from C. If AC is 1.4923 mi and BC is 1.0837 mi, and if C is 90°, find the measures of angles A and B.

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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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