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.sin 38° 42'

Verified step by step guidance

1. Convert the angle from degrees and minutes to decimal degrees. Recall that 1 degree = 60 minutes, so 42 minutes = 42/60 degrees.
2. Add the converted minutes to the degrees: 38 degrees + (42/60) degrees.
3. Use a calculator to find the sine of the angle in decimal degrees.
4. Ensure the calculator is set to degree mode before calculating the sine.
5. Round the result to six decimal places.

Key Concepts

Degrees and Minutes

In trigonometry, angles can be measured in degrees and minutes. One degree is divided into 60 minutes, which allows for more precise angle measurements. For example, 38° 42' means 38 degrees and 42 minutes. Understanding this notation is essential for converting the angle into a decimal format before performing calculations.

Trigonometric Functions

Trigonometric functions, such as sine, cosine, and tangent, relate the angles of a triangle to the ratios of its sides. The sine function, denoted as sin, specifically gives the ratio of the length of the opposite side to the hypotenuse in a right triangle. Knowing how to apply these functions is crucial for evaluating expressions involving angles.

Calculator Usage for Trigonometric Functions

Using a calculator to evaluate trigonometric functions requires understanding how to input angles correctly. Most calculators can operate in degrees or radians, so it is important to ensure the calculator is set to the correct mode. Additionally, knowing how to round answers to a specified number of decimal places is necessary for providing precise results.