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. cos 41° 24'

Key Concepts

Degrees and Minutes

In trigonometry, angles can be measured in degrees and minutes, where one degree is divided into 60 minutes. This notation is often used for greater precision in angle measurement. To convert an angle from degrees and minutes to decimal degrees, you can use the formula: decimal degrees = degrees + (minutes/60). Understanding this conversion is essential for accurately using a calculator to find trigonometric values.

Trigonometric Functions

Trigonometric functions, such as sine, cosine, and tangent, relate the angles of a triangle to the ratios of its sides. The cosine function, specifically, gives the ratio of the adjacent side to the hypotenuse in a right triangle. Knowing how to apply these functions is crucial for solving problems involving angles and their corresponding values, especially when using a calculator.

Calculator Usage for Trigonometric Functions

Using a calculator to find trigonometric values requires understanding the correct input format. Most calculators can compute trigonometric functions in either degree or radian mode, so it is important to ensure the calculator is set to the appropriate mode for the angle being used. Additionally, knowing how to simplify expressions before inputting them can lead to more accurate results, especially when dealing with complex angles.