Ch. 2 - Acute Angles and Right Triangles

Lial12th EditionTrigonometryISBN: 9780136552161Not the one you use?Change textbook

Lial 12th Edition

Ch. 2 - Acute Angles and Right Triangles

Problem 2.R.32

Chapter 3, Problem 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

Verified step by step guidance

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.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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.

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.

Recommended video:

5:31

Reference Angles on the Unit Circle

Related Practice

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. sec θ = 1.2637891

views

Textbook Question

Determine whether each statement is true or false. If false, tell why. Use a calculator for Exercises 39 and 42. sin 42° + sin 42° = sin 84°

views

Textbook Question

Find two angles in the interval [0°, 360°) that satisfy each of the following. Round answers to the nearest degree. tan θ = 1.3763819

views

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. cot 183° 48'

views

Textbook Question

Determine whether each statement is true or false. If false, tell why. Use a calculator for Exercises 39 and 42. 1 tan² 60° = sec² 60°

views

Textbook Question

Find two angles in the interval [0°, 360°) that satisfy each of the following. Round answers to the nearest degree. sin θ = 0.52991926

views