Ch. 2 - Acute Angles and Right Triangles

Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo

Lial 12th Edition

Ch. 2 - Acute Angles and Right Triangles

Problema 6

Capitolo 3, Problema 6

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.

cot 30°

Guida verificata passo dopo passo

Recall the definition of the cotangent function: \(\cot \theta = \frac{1}{\tan \theta}\) or equivalently \(\cot \theta = \frac{\cos \theta}{\sin \theta}\).

Identify the angle given: \(30^\circ\) is a special angle with well-known sine and cosine values.

Recall the sine and cosine values for \(30^\circ\): \(\sin 30^\circ = \frac{1}{2}\) and \(\cos 30^\circ = \frac{\sqrt{3}}{2}\).

Use the cotangent formula: \(\cot 30^\circ = \frac{\cos 30^\circ}{\sin 30^\circ} = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\).

Simplify the fraction by dividing the numerators and denominators to find the exact value of \(\cot 30^\circ\).

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Definition of Cotangent

Cotangent is the reciprocal of the tangent function, defined as cot(θ) = 1/tan(θ) or cot(θ) = adjacent/opposite in a right triangle. Understanding this helps in converting between tangent and cotangent values for given angles.

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Percorso guidato

5:37

Introduction to Cotangent Graph

Special Angles and Their Trigonometric Values

Certain angles like 30°, 45°, and 60° have well-known exact trigonometric values. Knowing these standard values allows quick evaluation of functions like cot 30°, which equals √3.

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Percorso guidato

3:28

Common Trig Functions For 45-45-90 Triangles

Reciprocal Identities in Trigonometry

Reciprocal identities relate pairs of trigonometric functions, such as cotangent being the reciprocal of tangent. These identities simplify calculations and help match functions to their values efficiently.

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Percorso guidato

5:32

Fundamental Trigonometric Identities

Pratica correlata

Domanda del libro di testo

CONCEPT PREVIEW 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.

csc 60°

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Domanda del libro di testo

Concept Check Match each angle in Column I with its reference angle in Column II. Choices may be used once, more than once, or not at all. See Example 1. I. II. 5. A. 45° 6. B. 60° 7. -135° C. 82° 8. D. 30° 9. E. 38° 10. F. 32°

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Domanda del libro di testo

Concept Check Match each angle in Column I with its reference angle in Column II. Choices may be used once, more than once, or not at all. See Example 1. I. II. 5. A. 45° 6. 212° B. 60° 7. C. 82° 8. D. 30° 9. E. 38° 10. F. 32°

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Domanda del libro di testo

Find one solution for each equation. Assume all angles involved are acute angles. cos(3θ + 11°) = sin( 7θ + 40°) 5 10

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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: 1.

sec 18°

Column II:

A. 88.09084757°