Textbook Question
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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Ch. 2 - Acute Angles and Right Triangles
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- 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
Chapter 3, Problem 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°)
Verified step by step guidance1
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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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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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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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3:35Intro 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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4:45How to Use a Calculator for Trig Functions
Related Practice
Textbook Question
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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Textbook Question
(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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Textbook Question
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.
tan θ = 6.4358841
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Textbook Question
Solve each problem. See Examples 1 and 2. Flying Distance The bearing from A to C is N 64° W. The bearing from A to B is S 82° W. The bearing from B to C is N 26° E. A plane flying at 350 mph takes 1.8 hr to go from A to B. Find the distance from B to C.
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Textbook Question
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. tan(-80° 06')
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