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

3. Unit Circle

Defining the Unit Circle

Trigonometry

3. Unit Circle

Defining the Unit Circle

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Problem 3.43

Textbook Question

Find a calculator approximation to four decimal places for each circular function value. See Example 3.
cot 6.0301

Verified step by step guidance

Understand that \( \cot \theta = \frac{1}{\tan \theta} \). Therefore, to find \( \cot 6.0301 \), you need to first find \( \tan 6.0301 \).

Use a calculator to find \( \tan 6.0301 \). Make sure your calculator is set to the correct mode (radians or degrees) based on the context of the problem.

Once you have \( \tan 6.0301 \), calculate \( \cot 6.0301 \) by taking the reciprocal: \( \cot 6.0301 = \frac{1}{\tan 6.0301} \).

Use the calculator to compute the reciprocal value to get \( \cot 6.0301 \).

Round the result to four decimal places as required.

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Key Concepts

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

Circular Functions

Circular functions, also known as trigonometric functions, relate the angles of a triangle to the lengths of its sides. The primary circular functions include sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). These functions are periodic and can be represented on the unit circle, where the angle corresponds to a point on the circle, allowing for the calculation of function values based on the angle's position.

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) for any angle θ where sin(θ) is not zero. The cotangent function is particularly useful in various applications, including solving triangles and analyzing periodic phenomena. Understanding how to compute cotangent values is essential for evaluating expressions like cot(6.0301).

Calculator Approximations

Calculator approximations involve using a scientific or graphing calculator to compute the values of trigonometric functions to a specified degree of accuracy, such as four decimal places. This process typically requires entering the angle in radians or degrees, depending on the calculator's settings. Mastery of this skill is crucial for obtaining precise values in trigonometric calculations, especially when dealing with non-standard angles like 6.0301 radians.