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'

Verified step by step guidance

1. Convert the angle from degrees and minutes to decimal degrees. Since there are 60 minutes in a degree, 48 minutes is equivalent to 48/60 degrees.
2. Add the converted minutes to the degrees to get the angle in decimal form: 183 + (48/60).
3. Use the identity \( \cot(\theta) = \frac{1}{\tan(\theta)} \) to express cotangent in terms of tangent.
4. Calculate \( \tan(183.8°) \) using a calculator.
5. Find \( \cot(183.8°) \) by taking the reciprocal of \( \tan(183.8°) \).

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 calculating values using a calculator.

Angle Conversion

In trigonometry, angles can be expressed in degrees, minutes, and seconds (DMS) or in decimal degrees. To simplify calculations, it is often necessary to convert DMS to decimal degrees. For example, 183° 48' can be converted to decimal degrees by calculating 183 + (48/60), which is crucial for accurate computation.

Calculator Functions

Modern calculators have specific functions for trigonometric calculations, including cotangent. It is important to ensure that the calculator is set to the correct mode (degrees or radians) based on the angle measurement used. Familiarity with using a calculator for trigonometric functions allows for precise evaluations of expressions like cot(183° 48').