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Use a calculator to approximate the value of each expression. Give answers to six decimal places. sec 222° 30'
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Ch. 2 - Acute Angles and Right Triangles
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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TOC.tableOfContents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 3, Problema 2.R.32
Find a value of θ, in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. cot θ = 1.1249386
Guida verificata passo dopo passo1
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: \(\tan \theta = \frac{1}{1.1249386}\).
Use the inverse tangent function to find \(\theta\): \(\theta = \tan^{-1} \left( \frac{1}{1.1249386} \right)\).
Make sure your calculator is set to degree mode since the problem asks for the angle in degrees.
Evaluate the inverse tangent expression to find \(\theta\) in degrees, and round your answer to six decimal places.
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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 used to relate angles to side lengths in trigonometry.
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Percorso guidato
5:37
Introduction to Cotangent Graph
Inverse Trigonometric Functions
Inverse trigonometric functions, such as arccotangent, allow us to find an angle when given a trigonometric ratio. Since cotangent is less common, the angle θ can be found by taking the arctangent of the reciprocal of the given cotangent value.
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Percorso guidato
4:28Introduction to Inverse Trig Functions
Angle Measurement and Interval Restrictions
Angles are often measured in degrees within specified intervals. Here, θ must lie in [0°, 90°), meaning the solution is an acute angle. This restriction ensures the angle corresponds to the first quadrant where cotangent values are positive.
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Percorso guidato
5:31Reference Angles on the Unit Circle
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