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°)

Key Concepts

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.