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. csc 145° 45'

Key Concepts

Cosecant Function

The cosecant function, denoted as csc, is the reciprocal of the sine function. It is defined as csc(θ) = 1/sin(θ). Understanding this relationship is crucial for simplifying expressions involving cosecant, as it allows you to convert csc into a more manageable form using sine values.

Angle Conversion

In trigonometry, angles can be expressed in degrees and minutes, where 1 degree equals 60 minutes. To work with angles in calculations, it is often necessary to convert them into decimal degrees. For example, 145° 45' can be converted to 145.75° by adding 45/60 to 145.

Calculator Usage for Trigonometric Functions

Using a calculator to evaluate trigonometric functions requires setting the correct mode (degrees or radians) based on the angle measurement. For this problem, since the angle is given in degrees, the calculator should be set to degree mode to ensure accurate results when calculating cosecant or any other trigonometric function.