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

1. Measuring Angles

Angles in Standard Position

Trigonometry

1. Measuring Angles

Angles in Standard Position

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2:25 minutes

Problem 25

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(90°-4.72°)

Verified step by step guidance

Recognize that \( \cot(90^\circ - \theta) \) is equivalent to \( \tan(\theta) \) due to the co-function identity for cotangent and tangent.

Substitute \( \theta = 4.72^\circ \) into the identity, so \( \cot(90^\circ - 4.72^\circ) = \tan(4.72^\circ) \).

Use a calculator to find \( \tan(4.72^\circ) \).

Ensure the calculator is set to degree mode before calculating.

Round the result to six 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.

Cotangent Function

The cotangent function, denoted as cot(θ), is the reciprocal of the tangent function. It is defined as cot(θ) = 1/tan(θ) or cot(θ) = cos(θ)/sin(θ). Understanding cotangent is essential for simplifying trigonometric expressions and solving problems involving angles.

Co-Function Identity

Co-function identities relate the trigonometric functions of complementary angles. For example, cot(90° - θ) = tan(θ). This identity is crucial for simplifying expressions involving angles that sum to 90 degrees, allowing for easier calculations and approximations.

Calculator Usage for Trigonometric Functions

Using a calculator to evaluate trigonometric functions requires understanding the angle mode (degrees or radians) set on the device. For this problem, ensuring the calculator is in degree mode is vital for accurately computing values like cot(90° - 4.72°) and obtaining results to the specified precision.