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 2.3.40

Capitolo 3, Problema 2.3.40

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. cot θ = 0.21563481

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Recall the definition of cotangent in terms of tangent: \(\cot \theta = \frac{1}{\tan \theta}\). This means \(\tan \theta = \frac{1}{\cot \theta}\).

Calculate \(\tan \theta\) by taking the reciprocal of the given cotangent value: \(\tan \theta = \frac{1}{0.21563481}\).

Use the inverse tangent function to find \(\theta\): \(\theta = \tan^{-1} \left( \frac{1}{0.21563481} \right)\).

Make sure your calculator is set to degree mode since the problem asks for the answer in degrees.

Evaluate the inverse tangent expression to find \(\theta\) in degrees, then round your answer to six decimal places as requested.

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Cotangent Function

The cotangent of an angle θ in a right triangle is the ratio of the adjacent side to the opposite side, or equivalently, cot θ = 1 / tan θ. It is the reciprocal of the tangent function and is defined for all angles where tan θ is not zero.

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Introduction to Cotangent Graph

Inverse Trigonometric Functions

To find an angle given a trigonometric ratio, we use inverse functions. For cotangent, θ = arccot(value), which can be computed as θ = arctan(1 / value). This allows us to determine the angle corresponding to a specific cotangent value.

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Introduction to Inverse Trig Functions

Angle Measurement and Interval Restrictions

The problem restricts θ to the interval [0°, 90°), meaning the angle must be in the first quadrant where all trigonometric ratios are positive. This constraint ensures a unique solution and affects how inverse functions are interpreted.

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Reference Angles on the Unit Circle

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