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.tan 421° 30'

Verified step by step guidance

1. Convert the angle from degrees and minutes to decimal degrees. Recall that 1 minute is equal to 1/60 of a degree.
2. Calculate the decimal degree equivalent: 421° 30' = 421 + 30/60 degrees.
3. Simplify the expression to get the angle in decimal degrees.
4. Use the tangent function on your calculator to find the tangent of the simplified angle.
5. Round the result to six decimal places as required.

Key Concepts

Angle Conversion

To work with angles in trigonometry, it's often necessary to convert between degrees and radians. In this case, the angle is given in degrees and minutes, which can be converted to decimal degrees by dividing the minutes by 60 and adding it to the degrees. Understanding this conversion is essential for accurate calculations using a calculator.

Trigonometric Functions

The tangent function, denoted as 'tan', is one of the primary trigonometric functions. It is defined as the ratio of the opposite side to the adjacent side in a right triangle. For angles greater than 360 degrees, the tangent function is periodic, meaning it repeats its values every 180 degrees, which is crucial for simplifying the expression before calculation.

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 in degrees, the calculator must be set to degree mode to ensure accurate results. Additionally, rounding the final answer to six decimal places is important for precision.