Skip to main content
Ch. 2 - Acute Angles and Right Triangles
Lial - Trigonometry 12th Edition
Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook
All textbooksLial 12th EditionCh. 2 - Acute Angles and Right TrianglesProblem 2.3.25
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 guidance
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.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2m
Was this helpful?

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.
Recommended video:
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.
Recommended video:
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.
Recommended video:
4:45
How to Use a Calculator for Trig Functions
Related Practice
Textbook Question

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.

893
views
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.

700
views
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.

725
views
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.

651
views
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.

sec θ = 1.1606249

633
views
Textbook Question

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.

sin 30°

494
views