Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

2. Trigonometric Functions on Right Triangles

Trigonometric Functions on Right Triangles

Trigonometry

2. Trigonometric Functions on Right Triangles

Trigonometric Functions on Right Triangles

Previous problemNext problem

0:51 minutes

Problem 64

Textbook Question

Determine whether each statement is possible or impossible. See Example 4. cot θ = ―6

Verified step by step guidance

Understand that the cotangent function, \( \cot \theta \), is defined as the reciprocal of the tangent function: \( \cot \theta = \frac{1}{\tan \theta} \).

Recall that the tangent function, \( \tan \theta \), can take any real number value, which means \( \cot \theta \) can also take any real number value except zero.

Since \( \cot \theta = -6 \) is a real number, it is possible for \( \cot \theta \) to equal \(-6\).

Consider the unit circle or the right triangle definitions to find an angle \( \theta \) where \( \cot \theta = -6 \).

Conclude that the statement \( \cot \theta = -6 \) is possible, as there exists an angle \( \theta \) for which this condition holds true.

Verified video answer for a similar problem:

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

Video duration:

51s

Play a video:

Was this helpful?

Key Concepts

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

Cotangent Function

The cotangent function, denoted as cot(θ), is the reciprocal of the tangent function. It is defined as cot(θ) = cos(θ) / sin(θ). The values of cotangent can range from negative to positive infinity, depending on the angle θ. Understanding this function is crucial for determining the feasibility of specific values, such as whether cot(θ) can equal -6.

Range of Trigonometric Functions

Each trigonometric function has a specific range of values it can take. For cotangent, the range is all real numbers, meaning it can take any value from negative to positive infinity. This concept is essential for evaluating whether a given statement about cotangent, like cot(θ) = -6, is possible or impossible based on the function's properties.

Trigonometric Identities

Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables involved. They help in simplifying expressions and solving equations. Familiarity with identities, such as cot(θ) = 1/tan(θ), allows for a deeper understanding of the relationships between different trigonometric functions, which is important when analyzing statements like cot(θ) = -6.